 # Probability & Statistics MCQs Part II

1) The regression lines are 4x-5y-33=0, 2x-9y+107=0 then find the mean
of x and y

a) 13, 17
b) 12, 13
c) 15, 13
d) none of these

2) a) b) c) d) 3) The tangent of the angle between the lines of regression y on x and x on
y is 0.6 and a) -0.5
b) 0.3
c) 0.5
d) -0.3

4) In a scatter diagram, if the plotted points form a straight line running
from the lower left to upper right corner, then there exists a

a) high degree of positive correlation
b) perfect positive correlation
c) perfect negative correlation
d) zero correlation

5) The regression coefficients are independent of
a) scale but not origin
b) origin but not scale
c) both origin and scale
d) neither of origin nor scale

6) A diagram obtained by plotting points, which are the set of observations obtained in a study of a population or sample, in which two characteristics are considered, is called
a) a line graph
b) a histogram
c) a scatter diagram
d) none of these

7) If r = 0, then
a) there is no relation between the variables
b) there is no linear relationship between the variables
c) both are false
d) both are true

8) If the variables x and y are connected by the relation ax+by+c = 0, then
the correlation between x and y is

a) +1 if a and b are of opposite sign
b) -1 if a and b are of same sign
c) +1 or -1 according as a and b are of the same sign or not
d) none of these

9) The Cov (x.y) between x and y if a) 3.2
b) 3.4
c) 3.3
d) 3.8

10) The coefficient of correlation between x and y for the data

x : 4 10 11 6 8
y : 2 6 12 3 4 is

a) 0.84
b) 0.83
c) 0.86
d) 0.81

11) Given :
No. of pairs of observations = 10
sum of deviations of x = -150
sum of deviations of y = – 30
sum of squares of deviations of x = 8000
sum of squares of deviations of y = 2000
sum of product of deviations of x and y = 3000
The Coefficient of Correlation, when the arbitrary means of x and y are 80
and 60 respectively is

a) 0.58
b) 0.68
c) 0.78
d) 0.61

12) If the regression equations are 3x=5-8y and 4y= 3-x, then the value  of
the correlation coefficient is

a) .814
b) -814
c) -.816
d) .816

13) The correlation between the variables `day temperature ` and `sale of ice
cream` is expect to be

a) negative
b) 0
c) positive
d) always and > – 1

14) If the regression equations are 2x+3y= 18 and 5x + y = 15, then which of
the following is false ?

a) b) c) d) 15) In the case of two variables, x and y, coefficient of correlation is equal to 1. Then the correlation between them is
a) perfect positive correlation
b) perfect negative correlation
c) high degree of positive correlation
d) none of these

16) The coefficient of correlation was defined by
a) Pascal
b) Laplace
c) Karl pearson
d) none of these

17) If coefficient of correlation r = – 1, then r is called
a) perfect and positive
b) perfect and negative
c) high degree of negative correlation
d) none of these

18) a) there exists no relationship between x and y
b) x and y are independent
c) there may exists a non-linear relationship between x and y
d) none of these

19) The coefficient of correlation is independent of
a) origin but not scale
b) scale but not origin
c) neither origin nor scale
d) both origin and scale

20) In a scatter diagram, if the plotted points form a straight line running
from the lower left to the upper right corner, then there exists a

a) high degree of positive correlation
b) perfect positive correlation
c) perfect negative correlation
d) none of these

21) In a scatter diagram, if the points fall in a narrow band from the upper
left corner to the lower right corner, there will be a

a) high degree of positive correlation
b) high degree of negative correlation
c) perfect negative correlation
d) none of these

22) If the point P(x, y) be equidistant from the points (a+b, b-a)and (a-b,
a+b) then

a) ax=by
b) ax=-by
c) ay=bx
d) ay=-bx

23) The value of correlation coefficient between two variables lies between
a) b) c) -1 and 1
d) 24) If the two variables x and y of a bivariate distribution have a perfect
correlation, they may be connected by

a) xy = 1
b) c) d) none of these

25) The coefficient of correlation between two variables x and y is 0. 5        their
covariance is 16 and S. D of x is 4, then the S.D of y is

a) 4
b) 8
c) 16
d) 64

26) If , then the cov.
(x,y) is equal to

a) 22
b) 2
c) -2
d) none of these

27) The value of standard deviation of x, when coefficient of correlation r
between two variables x and y is 0.82, covariance of x and y is 12.3
and the standard deviation of y is a) b) c) d) none of these

28) The values of covariance of two variables x and y is 148/3 and the  variance
of x = 272/3 and the variance of y is (131/3): Then the coefficient of correlation
is

a) .78
b) .87
c) .48
d) none of these

29)

For the observations

x 3 5 6 8 9
y 7 11 13 17 19
r is equal to

a) -1
b) 1
c) .93
d) none of these

30) For 10 observations on price (x) and supply (y), the following data were recorded, . Then
coefficient of correlation is given by

a) .957
b) .096
c) .472
d) none of these

31) If two variables have the linear relation ship x+ y = 50, the correlation
will be

a) 1
b) -1
c) 0.5
d) none of these

32) If coefficient of correlation r = 0.85, the S.D of x and y are respectively. Then the covariance of x and y is

a) 46.44
b) 4.644
c) 464.4
d) none of these

33) The value of spearman`s rank correlation coefficient for a certain
number of observations was found to be 2/3. The sum of squares of differences
between the corresponding ranks was 55. The number of pair is

a) 10
b) 9
c) 8
d) inconsistent

34) The variable x and y are connected by the equation ax + by + c = 0, ab>
0. Then coefficient of correlation between them is

a) 1
b) -1
c) 0
d) not defined

35) The regression coefficient of y on x is given by
a) b) c) d) none of these

36) be regression coefficients of x, on y, y on x and correlation coefficient
respectively, then

a) b) c) d) none of these

37) If r = 0, the regression lines are
a) parallel
b) c) perpendicular
d) none of these

38) The intersecting point of the two regression lines is
a) (0,0)
b) c) d) none of these

39) If a) 1/3
b) -1/3
c) 1/9
d) none of these

40) If the value of r will
be

a) .5
b) -.5
c) .25
d) none of these

41) If 2x+3y – 1 = 0 is the regression line of y on x, then is equal to

a) -3/2
b) -2/3
c) d) none of these

42) Two random variables have the least square regression lines 3x+2y
= 26 and 6x+y = 31. The coefficient of correlation between x and y is given
by

a) -.5
b) 0.5
c) .25
d) none of these

43) Covariance (x,y) between x and y if n = 10 is

a) 0.5
b) -0.4
c) -0.5
d) 0.4

44) Probability of getting heads in all four trials when a coin is tossed four times, is equal to
a) 1/4
b) 15/16
c) 1/16
d) none of these

45) Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is
a) 1/18
b) 1/12
c) 1/9
d) none of these

46) Two dice are thrown simultaneously. The probability of obtaining total score of seven is
a) 5/36
b) 6/36
c) 7/36
d) 8/36

47) The probability that a leap year selected at random contain 53 Sundays is
a) 7/366
b) 26/183
c) 1/7
d) 2/7

48) A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number, which is a square, is
a) 1/5
b) 2/5
c) 1/10
d) none of these

49) The probability of an event happening in one trial of an experiment is 0.6. Three independent trials are made. The probability that the event happens at least once is
a) 0.432
b) 0.064
c) 0.936
d) 0.568

50) One of the two exclusive events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are
a) 1 : 3
b) 3 : 1
c) 2 : 3
d) 3 : 2

51) Twelve coupons are numbered from 1 to 12. Six coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is less than or equal to 8, is
a) b) c) 1/33
d) none of these

52) Seven chits are numbered 1 to 7. Four are drawn one by one with replacements. The probability that the least number on any selected chit is 5, is
a) b) c) d) none of these

53) A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colours is
a) 47/66
b) 10/33
c) 5/22
d) none of these

54) The probabilities of three mutually exclusive events A, B and C are given by 2/3, 1/4 and 1/6 respectively. The statement
a) is true
b) is false
c) nothing can be said
d) could be either

55) A five-digit number is formed by the digits 1,2,3,4,5,6 and 8. The probability that the number has even digit at both ends is
a) 2/7
b) 3/7
c) 4/7
d) none of these

56) . An ordinary cube has 4 blank faces, one face marked 2 and another marked 3. Then the probability of obtaining 12 in 5 throws is
a) 5/1296
b) 5/1944
c) 5/2592
d) none of these

57) Three identical dice are rolled. The probability that the same number will appear on each of them is
a) 1/6
b) 1/18
c) 1/36
d) none of these

58) Three cards are drawn successively with replacement. The probability of selecting 2 aces and one king is
a) b) c) 1/13
d) none of these

59) If an integer p is chosen at random in the interval the probability that the roots of the equation are real is
a) 4/5
b) 2/3
c) 3/5
d) none of these

60) Two red, 4 white and 5 blue balls, balls of same colour are identical, are placed on a line at random. The probability that no two blue balls are consecutive is given by
a) 1/330
b) 1/22
c) 1/110
d) none of these

61) If A and B are such events that P (A) >0 and , then is equal to
a) 1 – P (A/B)
b) c) d) 62) There are 4 white and 4 black balls in a bag and 3 balls are drawn at random. If balls of same colour are identical, the probability that none of them is black, is
a) 1/4
b) 1/14
c) 1/2
d) none of these

63) Two events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.12. Then the probability that neither a nor B occurs is
a) 0.13
b) 0.38
c) 0.63
d) 0.37

64) A box contains 100 tickets numbered 1,2… 100. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The probability that the minimum number is 5 is
a) 13/15
b) 1/330
c) 1/3
d) 1/9

65) The odds in favour of a solving a problem are 3 to 4 and the odds against B solving the same problem are 5 to 7. If they both try the problem, the probability that the problem is solved is
a) 41/84
b) 16/21
c) 5/21
d) 1/4

66) 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) 241/1456
b) 164/4165
c) 451/884
d) none of these

67) A father has 3 children with at least one boy. The probability that he has 2 boys and one girl is
a) 1/4
b) 3/7
c) 1/3
d) none of these

68) From eighty cards numbered 1 to 80, two cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by
a) 21/316
b) 19/316
c) 1/4
d) none of these

69) A cubical dice is thrown 6 times. The probability that 2 and 4 will turn up exactly 3 times each is given by

a) b) c) d) none of these

70) The probability that an even A happens in one trial of an experiment is 0.7. Three independent trials of the experiment are performed. The probability that the even A happens at least once is
a) 0.657
b) 0.973
c) 0.189
d) none of these

71) Four any two independent events E1 and E2, is
a) b) c) d) none of these

72) Two players toss 4 coins each. The probability that they both obtain the same number of heads is
a) 5/256
b) 1/16
c) 35/128
d) none fo these

73) An experiment consists of 3 throws of a coin and success means 2 heads. The probability of no success, if experiment is repeated 3 times, is equal to
a) b) c) d) none of these

74) The probabilities of a problem being solved by two students are ½,1/3. The probability of the problem being solved is
a) 2/3
b) 4/3
c) 1/3
d) 1

75) Let A and B two events such that P (A)= 0.4, P (B)= 0.3 and P (AUB)=0.7. Then
a) A and B are independent
b) A and B are exhaustive
c) A and B are mutually exclusive
d) none of these

76) Three six faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is 8, is
a) 7/72
b) 7/54
c) 4/27
d) none of these

77) Probability of happening of at least one of the events is 0.6 and their simultaneous happening is 0.2. Then the value of P (A) + P (B) is
a) 0.8
b) 0.6
c) 0.2
d) 0.4

78) The probability that a man aged 50 years will die in a year is p. The probability that out of n men each aged 50 years, will die and be fist to die is
a) b) c) d) none of these

79) If the probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is
a) p + q
b) p + q – 2pq
c) p + p – pq
d) p + q + pq

80) A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six, The probability that it is actually a six is
a) 3/8
b) 1/5
c) 1/12
d) none of these

81) A dice and two coins are tossed. The probability that both the coins show heads and the dice shows 1 or 2, is
a) 7/12
b) 4/7
c) 1/12
d) none of these

82) An urn contains 8 blue and 4 green balls. Two balls are drawn at random. The probability that both balls are of the same colour (all balls are considered to be different) is
a) 17/33
b) 1/33
c) 14/33
d) 1/11

83) 8 blue and 4 green balls are contained in an urn. Balls of same colour
are identical. Two balls are drawn at random. The probability that both are
of the same colour is

a) 1/3
b) 2/3
c) 1/4
d) 3/4

84) From a pack of cards, 2 are drawn at random one by one with replacement. The probability that first is heart and 2nd is king is
a) b) c) d) none of these

85) If P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(AB) = 0.08, P(AC) = 0.28, P(ABC) = 0.09, , and P(BC) = x, then
a) b) c) d) none of these

86) If the letters of the word ASSASSIN are written down at random in a row, the probability that no two S’s occur together is
a) b) c) d) 87) A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 on the dice is:
a) b) c) d) none of these

88) For independent events A1…An, Then the probability that none of the events will occur is
a) n/(n+1)
b) n -1/(n+1)
c) 1/(n+1)
d) none of these

89) A dice is thrown. Consider two events A={1,2,3,4}, B={4,5,6}. Then the events A and B are
a) independent
b) dependent
c) mutually exclusive
d) exhaustive

90) A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. If is thrown twice. The probability that the sum of two numbers thrown is even is
a) 5/9
b) 4/9
c) 2/3
d) 1/3

91) The dice is tossed and you are told that either face 1 or 2 has turned up. Then the probability that it s face 1 is
a) 1/10
b) 6/21
c) 5/21
d) none of these

92) Let A be a set of 4 elements. Form the set of all functions from A to A, the probability that it is an into function is
a) 3/32
b) 29/32
c) 0
d) 1

93) 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) 1/3
b) 5/16
c) 1/4
d) 4/15

94) Host, his wife and 8 guests are to be seated on a round dining table at random. The probability that the host and his wife sit together is
a) 1/6
b) 2/9
c) 5/9
d) 1/10

95) The letters of the word ALLAHABAD are arranged at random. The probability that in the word so formed, all similar letters are found together, is
a) 1/63
b) 16/17
c) 5!/9!
d) none of these

96) Fifteen coupons are numbered 1,2… 15 respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is
a) (9/16) 6
b) (8/15) 7
c) (3/5)5
d) none of these

97) There are 5 volumes of mathematics among 25 books. They are arranged on a shelf in random order. The probability that the volumes of mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is
a) 1/5!
b) 50!/55!
c) 1/505
d) none of these

98) Let X ={1,2…50}, A subset A of X is choosen at random. The set X is reconstructed by replacing the elements of A, and another subset B of X is chosen at random. The probability that contains exactly 5 elements is
a) b) c) d) none of these

99) On a toss of two dice, A throws a total of 5. Then the probability that he will throw another 5 before he throws 7 is
a) 2/45
b) 2/5
c) 1/81
d) 1/9

100) . If A and B are two events such that then A and B are
a) mutually exclusive
b) dependent
c) independent
d) none of these