# Probability & Statistics MCQs Part V

**1) If and 2 P(A) = P(B) = p, then
the value of p is equal to**

**a)**

**b)**

**c)**

**d)**

**2) Two friends A and B have equal number of daughters. There are three cinema
tickets which are to be distributed among the daughters of A and B. The probability
that all the tickets go to daughters of A is .
The number of a daughters each of them have is**

**a)**4

**b)**5

**c)**6

**d)**3

**3) The probability that out of 10 persons, all born in April, at least two
have the same birthday is**

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

**4) are fifty real numbers
such that for r = 1, 2, 3 ……, 49.
Five numbers out of these are picked up at random. The probability that the
five numbers have as the middle
number is**

**a)**

**b)**

**c)**

**d)**none of these

**5) A second-order determinant is written down at random using the numbers 1,
-1 as elements. The probability that the value of the determinant is non-zero
is**

**a)**

**b)**

**c)**

**d)**none of these

**6) 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

**7) The probability that the birth days of six different persons will fall in
exactly two months is**

**a)**

**b)**

**c)**

**d)**

**8) A bag contains 16 coins of which two are counterfeit with heads on both
sides. The rest are fair coins. One is selected at random from the bag and
tossed. The probability of getting a head is**

**a)**

**b)**

**c)**

**d)**none of these

**9) A book contains 1000 pages. A page is chosen at random. The probabilities
that the sum of the digits of the marked number on the page is equal to 9
is**

**a)**

**b)**

**c)**

**d)**none of these

**10) A fair die is tossed eight times. The probability that a third six is observed
on the eight throw is**

**a)**

**b)**

**c)**

**d)**none of these

**11) The sum of two positive quantities is equal to 2 n.
The probability that their product is not less than
times their greatest product is**

**a)**

**b)**

**c)**

**d)**none of these

**12) Four tickets marked 00, 01, 10, 11 respectively
are placed in a bag. A ticket is drawn at random five times, being replaced
each time, the probability that the sum of the numbers on tickets thus
drawn is 23, is**

**a)**

**b)**

**c)**

**d)**none of these

**13) A committee of five is to be chosen from a group
of 9 people. The probability that a certain married couple will either
serve together or not at all is**

**a)**

**b)**

**c)**

**d)**

**14) A drawer contains 5 brown socks and 4 blue socks
well mixed. A man reaches the drawer and pull out 2 socks at random. The
probability that they will match is**

**a)**

**b)**

**c)**

**d)**

**15) If m rupee coins and n ten paise coins are placed
in a line, then the probability that the extreme coins are ten paise coins
is**

**a)**

**b)**

**c)**

**d)**

**16) In shuffling a pack of playing cards, four are
accidentally dropped. The probability that the missing cards should be
one from each suit is**

**a)**

**b)**

**c)**

**d)**none of these

**17) Dialing a telephone number an old man forgets
the last two digits remembering only that these are different, dialled
at random. The probability that the number dialed correctly is**

**a)**

**b)**

**c)**

**d)**none of these

**18) If n integers taken at random are multiplied together,
then the probability that the last digit of the product is 1,3,7 or 9
is**

**a)**

**b)**

**c)**

**d)**none of these

**19) If n integers taken at random are multiplied
together, then the probability that the last digit of the product is 2,4,
6 or 8 is **

**a)**

**b)**

**c)**

**d)**none of these

**20) **

**Four positive integers are taken at random and are**

multiplied together. Then the probability that the product ends in an odd

digit other than 5 is

multiplied together. Then the probability that the product ends in an odd

digit other than 5 is

**a)**

**b)**

**c)**

**d)**

**21) A bag contains 50 tickets numbered 1,2,3,…50 of which
five are drawn at random and arranged in ascending order of magnitude **

**a)**

**b)**

**c)**

**d)**none of these

**22) An ordinary cube has four blank faces, one face marked
2 and another marked 3. Then the probability of obtaining 9 in 5 throws is **

**a)**

**b)**

**c)**

**d)**

**23) The probability that the 13 ^{th} day of a
randomly chosen month is a Friday, is**

**a)**

**b)**

**c)**

**d)**none of these

**24) The chance of an event happening is the square of
the chance of a second event but the odds against the first are the cube of
the odds against the second. The chances of the events are**

**a)**

**b)**

**c)**

**d)**none of these

**25) The probability that a leap year selected at random
contains either 53 Sundays or 53 Mondays, is**

**a)**

**b)**

**c)**

**d)**

**26) **

If the mean of the set of numbers x_{1} ,

x_{2} , ……… x_{n} is x,

then the mean of the numbers x_{i} + 2i , 1**a)** **b)** **c)** **d)**

**27) The weighted A. M of first n natural numbers whose weights are equal to the corresponding numbers is equal to****a)** 2n + 1**b)** **c)** **d)** 2n + 1/6

**28) **

**The sum of deviation of a set of values x _{1}
, x_{2} ,……..x_{n} measured from 50 is
-10 and the sum of deviation of values from 46 is 70.
The value of n and t**

**a)**20, 49.5

**b)**20, 49

**c)**21, 39.5

**d)**None of the given

**29) **

The arithmetic mean of a set of observation is x

. If each observation is divided by b and then it is

increased by 12, then the mean of the new**a)** **b)** **c)** **d)**

**30) ****a)** n**b)** **c)** n + 2**d)**

**31) **

The mean of n items is X

. If the first item is increased by 1, second by 2 and so on , then the

new mean is

**a)**

X + n

**b)** **c)** **d)** None of the given

**32) ****a)** nq**b)** np**c)** n ( p + q )**d)** None of the given

**33) The mean monthly salary paid to 75 employees in a company is Rs 1420. The mean salary of 25 of them is Rs 1350 and that of 30 others is Rs 1425. The mean salary of the remaining is****a)** 1400**b)** 1450**c)** 1500**d)** None of the given

**34) The average score of girls in class X examination of the school is 71.8. The % of boys in class X of the school is****a)** 40 %**b)** 60 %**c)** 30 %**d)** 65 %

**35) A train travels first 300 kilometers at an average rate of 30 k. p. h and and further travels the same distance at an average of 40 k. p. h. The average speed over the whole distance is****a)** 34.29**b)** 33.29**c)** 35.25**d)** 34.25

**36) **

If G is the G.M of the product of r set of

observations with geometric means G_{1} , G_{2}

…… G_{r} respectively, then G is equal to

**a)**

log G_{1} + log G_{2} + ……. +

log G_{r}

**b)**

G_{1} . G_{2} ………G_{r}

**c)**

log G_{1} . log G_{2} ……..log G_{r}

**d)** None of the given

**37) If a linear relation a X + b Y + C = 0 exists between the variables X and Y and ab < 0 , then the coefficient of correlation between X and Y is****a)** 1**b)** -1**c)** 0**d)** any number between -1 and 1

**38) Let X and Y be two variables with the same variance and U and V be two variables such that U = X + Y , V = X – Y Then Cov (u , V ) is equal to****a)** Cov ( X, Y)**b)** 0**c)** 1**d)** -1

**39) If X and Y are two uncorrelated variables and if U = X + Y , V = X – Y then r ( U , V ) is equal to****a)** **b)** **c)** **d)** None of the given

**40) If X and Y are two independent variables with means 5 and 10 and variances 4 and 9 respectively . If u = 3 X + 4 y and V = 3 X – Y, then r ( U, V ) is equal to****a)** 0**b)** 1**c)** **d)** None of the given

**41) If the line of regression of Y on X and X on Y are respectively y = Kx + 4 and x = 4 y + 5 , then****a)**

0 ú k ú

4

**b)** **c)** **d)** None of the given

**42) **

If the lines of regression of Y on X and X on Y

make angles 30^{o} and 60^{o} respectively with the

positive direction of x-axis, then the correlation coefficient between X and Y

is

**a)** 1**b)** -1**c)** **d)**

**43) **

Let X and Y be two variables with the same mean. If the

lines of regressions of Y on X and X on Y are respectively y

= ax + b and x = a**a)** **b)** **c)** **d)**

**44) Experiments show that radium disintegrates at a rate proportional to the amount of radium present at the moment. Its half life is 1590 years. The percentage it will disappear in one year is****a)** 0.03 %**b)** 0.04 %**c)** 0.05 %**d)** 0.02 %

**45) ****a)** 2**b)** 5**c)** 8**d)** None of the given

**46) Let X and Y be two variables with the same variance and U and V be two variables such that U = X + Y , V = X – Y . Then Cov ( U , V ) is equal to****a)** Cov ( X, Y )**b)** 0**c)** 1**d)** -1

**47) If a linear relation a X + bY + c = 0 exists between the variables X and Y ab < 0, then the coefficient of correlation between X and Y is****a)** -1**b)** 0**c)** 1**d)** any number between -1 and 1

**48) If X and Y are two uncorrelated variables and if u = X + Y , v = X – Y then r ( u, v ) is equal to****a)** **b)** **c)** **d)** None of the given

**49) If x and Y are two independent variables with means 5 and 10 and variance 4 and 36 respectively. If U = 6 X + 4 Y and v = 6X – Y, then r ( u, v ) is equal to****a)** 0**b)** 1**c)** -1**d)** 0.5

**50) ****a)** -1**b)** 1**c)** -0.82**d)** None of the given

**51) 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)**

**52) **

If E and F are events

with P (E) ú P (F)

and P ( E ¦ F) > 0 then

**a)**

occurrence of E ¦

occurrence of F

**b)**

occurrence of F ¦

occurrence of E

**c)**

Non-occurrence of E ¦

Non – occurrence of F

**d)**

None of the above implications holds.

**53) A fair coin is tossed repeatedly if tail appears on first four tosses, then the probability of head appearing on fifth toss equals****a)** **b)** **c)** **d)**

**54) If four dice are thrown together, then the probability that the sum of the numbers appearing on them is 13, is****a)** **b)** **c)** **d)**

**55) Six faces of a die are marked with the numbers 1, -1, 0, -2, 2 and 3 . The die is thrown thrice . The probability that the sum of the numbers thrown is six, is****a)** **b)** **c)** **d)**

**56) The probabilities that a student passes in Mathematics, Physics, and Chemistry are m, P and C, respectively of these subjects, the student has 75% chance of passing in at least one, a 50% chance of passing in at least two, and a 40 % chance of passing in****a)** (a)**b)** (b)**c)** (c)**d)** Both (b) and (c)

**57) If m rupee coins and n ten paise coins are placed in a line , then the probability that the extreme, coins are ten paise coins is****a)** **b)** **c)** **d)**

**58) ****a)** **b)** **c)** **d)**

**59) ****a)** **b)** **c)** **d)** None of the given

**60) India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0,1 and 2 are 0.45 , 0.05 and 0.50 respectively. Assuming that out comes are independent , the probability of India getting at least 7 poi****a)** 0.8750**b)** 0.0875**c)** 0.0625**d)** 0.0250

**61) If A and B are independent events such that P (A) > 0 áP (B) > 0, then****a)** A and B are mutually exclusive**b)** **c)** **d)**

**62) For any two events A and B in a sample space****a)** **b)** **c)** **d)**

**63) A speaks truth in 60% cases and B speaks truth in 70% cases. The probability that they will say the same thing while describing single event is****a)** 0.56**b)** 0.54**c)** 0.38**d)** 0.94

**64) A letter is taken out at random from \’ASSISTANT\’ and another is taken out from \’STATISTICS\’. The probability that they are the same letter is****a)** **b)** **c)** **d)** None of the given

**65) **

Odds in favour of an event A are 2 to 1 and

odds in favour of A + B are 3 to 1.Consistent with

this information the smallest and largest values for the probability of event B

are given by**a)** **b)** **c)** **d)** None of the given

**66) The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second . The chances of the events are****a)** **b)** **c)** **d)** None of the given

**67) If a party of n person sit at a round table, then the odds against two specified individuals sitting next to each other are****a)** 2 : n – 3**b)** n – 3 : 2**c)** n – 2 : 2**d)** 2 : n – 2

**68) If the letter of the word MISSISSIPPI áare written down at random in a row, the probability that four S\’s come consecutively is****a)** **b)** **c)** **d)** None of the given

**69) A bag contains m white and n black balls. Two players A and B alternately draw a ball from the bag, replacing the ball each time after draw. A begins the game . If the probability of the probability of A winning ( that is drawing a white ball ) is twice t****a)** 1 : 2**b)** 2 : 1**c)** 1 : 1**d)** None of the given

**70) A bag contains an assortment of blue and red balls. If two balls are drawn at random, the probability of drawing two red balls is five times the probability of drawing two blue balls. Furthermore, áthe probability of drawing one ball of each colour is si****a)** 6, 3**b)** 3, 6**c)** 2, 3**d)** None of the given

**71) A coin is tossed three times. The probability of getting head and tail alternately is****a)** **b)** **c)** **d)** None of the given

**72) One ticket is selected at random from 100 tickets numbered 00, 01, 02, ——– 99. Suppose A and B are the sum and product of the digit found on the ticket . Then P ( A = 7 / B = 0 ) is given by****a)** 2 / 13**b)** 2 / 19**c)** 1 / 50**d)** None of the given

**73) If A and B each toss three coins. The probability that both get the same number of head is****a)** **b)** **c)** **d)**

**74) A fair coin is tossed a fixed number of times. If the probability of getting 4 heads equals the probability of getting 7 heads, áthen the probability of getting 2 heads is****a)** **b)** **c)** **d)**

**75) An experiment succeeds twice as often as it falls. The probability that in the next six trials there are at least 4 successes, is****a)** **b)** **c)** **d)**

**76) Four tickets marked 00, 01, 10, 11 respectively are placed in a bag. A ticket is drawn at random five times, being replaced each time. The probability that the sum of the numbers on tickets thus drawn is 23, is****a)** 25 / 256**b)** 100 / 256**c)** 231 / 256**d)** None of the given

Answers

Great post! it helped me a lot. Thank you, may God bless you.