# Probability & Statistics MCQs Part IV

**1) A die is thrown 4 times. Probability of getting at most two 6 is****a)** 0.984**b)** 0.802**c)** 0.621**d)** 0.721

**2) A man alternately tosses a coin and throws a die. The probability of his
getting a head on the coin before he gets 4 on the die is**

**a)**

**b)**

**c)**

**d)**

**3) A random variable x is defined byThen
E(x) is**

**a)**6

**b)**7

**c)**5

**d)**8

**4) A and B are two independent events. The probability that both A and B occurs
is and the probability that neither
of them occurs is . Then the probability
of the two events are respectively.**

**a)**

**b)**

**c)**

**d)**

**5) The probability that a person will hit a target in shooting practice is
0.3. If he shoots 10 times, then the probability of his shooting the target
is**

**a)**1

**b)**

**c)**

**d)**

**6) Two dice are thrown, the probability that the sum of the points on two dice
will be 7 is**

**a)**

**b)**

**c)**

**d)**

**7) The least number of times a fair coin must be tossed so that the probability
of getting at least one head is at least 0.8 is**

**a)**7

**b)**6

**c)**5

**d)**none of these

**8) A fair coin is tossed 100 times. The probability of getting tails an odd
number of times is**

**a)**

**b)**

**c)**

**d)**none of these

**9) A determinant is chosen at random from the set of all determinants of order
2 with elements 0 or 1 only. The probability that the determinant chosen is
non-zero is**

**a)**

**b)**

**c)**

**d)**none of these

**10) The mean and variance of a binomial variate X are 2 and 1 respectively,
then the probability that X takes a value greater than 1 is**

**a)**

**b)**

**c)**

**d)**

**11) A speaks truth in 60 percent cases and B speaks truth in 70 percent cases.
The probability that they will say the same thing while describing a single
event is**

**a)**0.56

**b)**0.54

**c)**0.38

**d)**0.94

**12) India plays two matches each with West Indies and Australia. In any match
probabilities of India getting points 0,1 and 2 are 0.45, 0.05 and 0.50 respectively.
Assuming that the outcomes are independent, the probability of India getting
at least 7 points is**

**a)**0.8750

**b)**0.0875

**c)**0.0625

**d)**0.0250

**13) The probability that a man lives after 10 years is and
that his wife is alive after 10 years is .
The probability that neither or them is alive after 10 years is**

**a)**

**b)**

**c)**

**d)**

**14) The probability of occurrence of an event A is .
The probability of non-occurrence of the event B is .
The probability that al least one of them will occur **

**a)**

**b)**

**c)**

**d)**0.8

**15) The probability of reaching an item at a site is 0.9. The probability
of getting at least 4 items out of a total of 5 items is**

**a)**

**b)**

**c)**

**d)**none of these

**16) Probabilities that a plant will live is
and the probability that another plant lives is .
The probability that only one of them lives is**

**a)**

**b)**

**c)**

**d)**none of these

**17) The probability that a teacher will give an unannounced test during
any class meeting is .
If a student is absent twice, then the probability that the student will
miss at least one test is**

**a)**

**b)**

**c)**

**d)**

**18) If in a distribution each x is replaced by corresponding value of f(x),
then the probability of getting whose
original probability is is**

**a)**

**b)**

**c)**

**d)**none of these

**19) In 324 throws of 4 dice, the expected number of times three sixes occur
is**

**a)**81

**b)**5

**c)**9

**d)**31

**20) Two players of equal skill are playing a set of games. They leave off
when A requires 3 points to win and B requires 2 points to win. If the stake
was Rs. 32, what share would each take**

**a)**9:23

**b)**16:16

**c)**10:22

**d)**none of these

**21) A sample space consists of three mutually exclusive and equally likely
events. The probability of happening of each one of them is equal to**

**a)**0

**b)**

**c)**1

**d)**none of these

**22) For any two independent events
and
in a space S, Pif **

**a)**

**b)**

**c)**

**d)**

**23) A coin is tossed successively three times. The probability of getting
exactly 2 heads is:**

**a)**

**b)**

**c)**

**d)**

**24) The probability of guessing correctly at least 8 out of 10 answers
on a true-false examination is**

**a)**

**b)**

**c)**

**d)**

**25) From a well-shuffled pack of 52 cards, w cards are drawn, the first
being replaced before the second is drawn. The probability that the first
in a diamond and the second is queen is**

**a)**

**b)**

**c)**

**d)**

**26) For a B.D., the parameters n and p are 16 and
respectively. Then its S.D. s is equal to**

**a)**2

**b)**

**c)**

**d)**4

**27) Let A, B, C be three equally and collectively exhaustive events. If
the odds are 8:3 against A, 5:2 against B, then the odds against C are**

**a)**20:17

**b)**50:31

**c)**43:34

**d)**77:34

**28) The probability that Krishna will be alive 10 years hence is
and Hari will be alive is .
What is the probability that both Krishna and Hari will be dead 10 years
hence?**

**a)**

**b)**

**c)**

**d)**

**29) Let E and F be two independent events. The probability that both E
and F happen is
and the probability that neither E nor F happen is .
Then**

**a)**

**b)**

**c)**

**d)**

**30) An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four
times. Out of four values obtained, the probability that the minimum face
value is not less than 2 and the maximum face value is not greater than
5 is:**

**a)**

**b)**

**c)**

**d)**

**31) A binary number is made up of 8 digits. Suppose that the probability
of an incorrect digit appearing is p and that the errors in different digits
are independent of each other. Then the probability of forming an incorrect
number is:**

**a)**

**b)**

**c)**

**d)**

**32) If the probability for A to fail in an examination is 0.2 and that
for B is 0.3, then the probability that either A or B fails is:**

**a)**0.38

**b)**0.44

**c)**0.50

**d)**0.94

**33) A man has 3 pairs of black socks and 2 pairs of brown socks kept together
in a box. If he dresses hurriedly in the dark, the probability that after
he has put on a black sock, he will then put on another black sock is:**

**a)**

**b)**

**c)**

**d)**

**34) The chance of throwing a total of 3 or 5 or 11 with two dice is****a)** **b)** **c)** **d)**

**35) Four persons are chosen at random from a group containing 3 men, 2
women, and 4 children. The chance that exactly 2 of them will be children
is**

**a)**

**b)**

**c)**

**d)**

**36) A rifleman is firing at a distance target and has only 10% chance of
hitting it. The number of rounds, he must fire in order to have more than
50% chance of hitting it at least once is**

**a)**5

**b)**7

**c)**9

**d)**11

**37) A box contains 3 white and 2 red balls. If we draw one ball and without
replacing the first ball, the probability of drawing red ball in the second
draw is**

**a)**

**b)**

**c)**

**d)**

**38) If
and then
lies in the interval**

**a)**[.30, .80]

**b)**[.35, .75]

**c)**[.40, .70]

**d)**[.45, .65]

**39) A and B are two events such that ,
then
is equal to**

**a)**

**b)**

**c)**

**d)**

**40) Given two events A and B. If odds against A are as 2:1 and those in
favour of
are as 3:1, then**

**a)**

**b)**

**c)**

**d)**none of these

**41) Let X and Y be two random variables. The relationship .
E(Y) holds**

**a)**Always

**b)**If E(X+Y)=E(X)+E(Y) is true

**c)**If X and Y are independent

**d)**If X can be obtained from Y be a linear transformation

**42) A Binomial Probability Distribution is symmetrical if p, the probability
of success in a single trial is**

**a)**

**b)**

**c)**

**d)**less than q where q = 1 – p

**43) A coin is tossed three times in succession. If E is the event that
there are at least two heads and F is the event in which first throw is
a head, Then P(E/F) =**

**a)**

**b)**

**c)**

**d)**

**44) In a box there are 2 red, 3 black and 4 white balls. Out of these three
balls are drawn together. The probability of these being of same colour
is**

**a)**

**b)**

**c)**

**d)**none of these

**45) The probability that a non-leap year has 53 Sundays is****a)** **b)** **c)** **d)**

**46) In tossing 10 coins the probability of getting exactly 5 heads is****a)** **b)** **c)** **d)**

**47) The probability that a company executive will travel by train is and
that he will travel by plane is .
The probability of his traveling by train or plane is:**

**a)**

**b)**

**c)**

**d)**

**48) Seven white balls and three black balls are randomly placed in a row.
The probability that no two black balls are placed adjacently equals**

**a)**

**b)**

**c)**

**d)**

**49) If from each of the three boxes containing 3 white and 1 black, 2 white
and 2 black, 1 white and 3 black balls, one ball is drawn at random, then
the probability that 2 white and 1 black ball will be drawn is**

**a)**

**b)**

**c)**

**d)**

**50) If
and
are complementary events of events, E and F respectively and 0<P(F)<1,
then**

**a)**

**b)**

**c)**

**d)**none of these

**51) There are four machines and it is known that exactly two of them are
faulty. They are tested, one by one, in a random order till both the faulty
machines are identifies. Then the probability that only two tests are needed
is**

**a)**

**b)**

**c)**

**d)**

**52) If E and F are events with P(E)£ P(F)
and P(EÇ F)>0, then**

**a)**

**b)**

**c)**

**d)**none of the above implication holds

**53) A fair coin is tosses repeatedly. If tail appears on first four tosses,
then the probability of head appearing on fifth toss equals**

**a)**

**b)**

**c)**

**d)**

**54) 5 persons entered the lift cabin on the ground floor of an 8 floor
house. Suppose that each of them independently and with equal probability
can leave the cabin at any floor beginning with the first, then the probability
of all 5 persons leaving at different floors is**

**a)**

**b)**

**c)**

**d)**

**55) If A and B are independent events such that 0 < P (A) < 1 and
0 < P (B) < 1, then which one is not correct****a)** A and B are mutually exclusive**b)** **c)** **d)**

**56) If the integers m and n are chosen at random between 1 and 100, then
the probability that a number of the form
is divisible by 5 equals is **

**a)**

**b)**

**c)**

**d)**

**57) If E _{1}denote the event of coming sum 6 in throwing of two
dice and E_{2} be the event of coming 2 in any one of the two,
then is**

**a)**

**b)**

**c)**

**d)**none of the above

**58) Three letters are drawn from the alphabet of 26 letters without replacement.
The probability that they appear in alphabetical order is**

**a)**

**b)**

**c)**

**d)**

**59) The probability that the three cards drawn from a pack of 52 cards
are all red is**

**a)**

**b)**

**c)**

**d)**

**60) Let p be the probability of happening any event and q its failure,
then the total chance of r successes in n trials is**

**a)**

**b)**

**c)**

**d)**

**61) The mean and variance of a Binomial distribution are 6 and 4. The parameter
n is**

**a)**18

**b)**12

**c)**10

**d)**9

**62) A coin is tossed 4 times. The probability that at least one head turns
up is**

**a)**

**b)**

**c)**

**d)**

**63) A box contains 6 nails and 10 nuts. Half of the nails and half of the
nuts are rusted. If one item is chosen at random, the probability that it
is rusted or is a nail is**

**a)**

**b)**

**c)**

**d)**

**64) A box contains 10 good articles and 6 with defects. One item is drawn
at random. The probability that it is either good or has a defect is**

**a)**

**b)**

**c)**

**d)**

**65) The probability that a student passes in Mathematics, Physics, Chemistry
are m, p, c respectively. Of these subjects, the student has 75% chance
at passing in at least one, a 50% chance of passing in at least two and
a 40% chance of passing in exactly two. Which of the following relations
is true?**

**a)**

**b)**

**c)**

**d)**none of these

**66) The probability of occurrence of multiple of 2 on one dice and a multiple
of 3 on the other dice if both are thrown together is**

**a)**

**b)**

**c)**

**d)**

**67) If P(A)=0.2 and P(B)=0.5, then****a)** **b)** **c)** **d)**

**68) A bag contains 5 brown and 4 white socks. A man pulls out two socks.
The probability that these are of the same colour is**

**a)**

**b)**

**c)**

**d)**

**69) Probability of throwing three dice to get equal numbers on the face
is**

**a)**

**b)**

**c)**

**d)**

**70) A box contains 24 identical balls of which 12 are white and 12 black. The
balls are drawn at random from the box one at a time with replacement. The
probability that a white ball is drawn for the 4**

^{th}time on the 7

^{th}draw is

**a)**

**b)**

**c)**

**d)**

**71) Four digit numbers are formed using each of the digits 1, 2 ………., 8 only
once. One number from these is picked up at random. The probability that the
selected number contains unity is**

**a)** **b)** **c)** **d)** none of these

**72) From a bag containing 9 distinct white and 9 distinct black balls, 9 balls
are drawn at random one by one, the drawn balls being replaced each time.
The probability that at least four balls of each colour is in the draw, is**

**a)**

**b)**

**c)**

**d)**none of these

**73) Cards are drawn one by one at random from a well-shuffled pack of 52
playing cards until 2 aces are obtained for the first time. The probability
that 18 draws are required for this is**

**a)**

**b)**

**c)**

**d)**none of these

**74) A person draws a card from a pack, replaces it, shuffles the pack, again
draws a card, replaces it and draws again. This he does until he draws a heart.
The probability that he will have to make at least four draws is**

**a)**

**b)**

**c)**

**d)**none of these

**75) A and B throw a dice. The probability that A`s throw is not greater than
B`s is**

**a)**

**b)**

**c)**

**d)**

**76) Let 0 < P (A) < 1, 0 < P (B) < 1 and ****a)** P(B/A) = P(B)-P(A)**b)** **c)** **d)** P (A/B) = P (A) + P (B)

**77) The probability of India winning a test match against West Indies is .
Assuming independence from match to match, the probability that in a 5 match
series India`s second win occurs at third test is**

**a)**

**b)**

**c)**

**d)**

**78) The probability that the four S`s come consecutively in the word MISSISSIPPI
is**

**a)**

**b)**

**c)**

**d)**none of these

**79) A car is parked by an owner amongst 25 cars in a row, not at either end.
On his return he finds that exactly 15 places are still occupied. The probability
that both the neighbouring places are empty is
**

**a)**

**b)**

**c)**

**d)**none of these

**80) The probability that when 12 balls are distributed among three boxes, the
first will contain three balls is**

**a)** **b)** **c)** **d)** none of these

**81) A bag contains 4 tickets numbered 1, 2, 3, 4 and another contains 6 tickets
numbered 2, 4, 6, 7, 8, 9. If one bag is chosen at random and two tickets
are drawn from the chosen bag, the probability that the tickets drawn bear
even numbers is**

**a)**

**b)**

**c)**

**d)**none of these

**82) A and B are any two mutually exclusive events, then**

**a)** **b)** **c)** P(A)

**d)** none of these

**83) There are 8 coloured balls and correspondingly 8 coloured (same as the balls)
bags. The balls are placed in the bags, each one in one bag. The probability
that 5 of the balls are placed in the respective coloured bags is**

**a)**

**b)**

**c)**

**d)**none of these

**84) A person has a bunch of n keys, only one of which exactly fits a
lock. The person tries to open the lock by trying the keys at random. The
probability that he opens the lock at the kth attempt on the assumption
that he rejects the keys already tried is**

**a)**

**b)**

**c)**

**d)**

**85) A six faced die is so biased that it is twice likely to show an even number
as compared to an odd number when thrown. The die is thrown twice. The probability
that the sum of the two numbers is even is
**

**a)**

**b)**

**c)**

**d)**none of these

**86) In order to get at least once a head with ,
the number of times a coin needs to be tossed is**

**a)**3

**b)**4

**c)**5

**d)**none of these

**87) From 4 children, 2 women and 4 men, 4 are selected. The probability that
there are exactly 2 children among the selected is**

**a)**

**b)**

**c)**

**d)**none of these

**88) In throwing of two dice, the probability of getting a multiple of 4 is****a)** **b)** **c)** **d)** none of these

**89) Two red, 4 white and 5 blue balls (balls of the same colour are identical)
are placed on a line at random. The probability that no two blue balls are consecutive,
is given by**

**a)**

**b)**

**c)**

**d)**none of these

**90) A die and two coins are tossed. The probability that both the coins show
heads and the die shows 1 or 2 is**

**a)**

**b)**

**c)**

**d)**none of these

**91) A number of five digits is formed with the digits 0, 1, 2, 3, 4 without
repetition. The probability that it is a number divisible by 4 is**

**a)**

**b)**

**c)**

**d)**

**92) Two digits are selected at random from the digits 1 to 9. If their sum is
even, the probability that both the numbers are odd, is**

**a)**

**b)**

**c)**

**d)**

**93) An integer is chosen at random from the number 1, 2, 3, ….., 25. The probability
that the chosen number is divisible by 3 or 4 is:**

**a)**

**b)**

**c)**

**d)**

**94) For a random variable X, the sum of the probabilities is always a real number
p such that**

**a)**p = 0

**b)**p = 1

**c)**0 < p < 1

**d)**p > 0

**95) A fair die is tossed 180 times. The S.D. of the number of sixes is****a)** **b)** 5**c)** 25**d)** 30

**96) Out of 13 applicants for a job, there are 5 women and 8 men. It is desired
to select 2 persons for the job. The probability that at least one of the
selected persons will be a women is**

**a)**

**b)**

**c)**

**d)**

**97) Cards are drawn from a pack of 52 cards one by one. The probability that
exactly 10 cards will be drawn before the first ace is**

**a)**

**b)**

**c)**

**d)**none of these

**98) An unbiased die with faces, 1, 2, 3, 4, 5 and 6 is thrown 4 times. Out of
four face values obtained the probability that the minimum face value is not
less than 2 and the maximum face value is not greater than 5 is**

**a)**

**b)**

**c)**

**d)**

**99) A number is chosen at random among the first 120 natural numbers. The probability
that the number chosen being a multiple of 5 or 15 is**

**a)**

**b)**

**c)**

**d)**none of these

**100) A and B stand in a line at random with 10 other people. The probability
that there will be 3 people between them is**

**a)**

**b)**

**c)**

**d)**none of these

**Answers**