61. A traffic office imposes on an average 5 number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follows a Poisson distribution. The probability that there will be less than 4 penalties in a day is

62. Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is

63. Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has a probability 1/5 of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office is

64. In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is

65. Consider a dice with the property that the probability of a face with n dots showing up is proportional to n. The probability of the face with three dots showing up is

66. A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n-3) is

- 2
^{-n} - 0
- 2
^{-n+3} ^{n}C_{n-3}2^{-n}

67. A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

- 1/3
- 1/2
- 2/3
- 3/4

68. A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Give that the first removed ball is white, the probability that the second removed ball is red is

- 1/3
- 3/7
- 1/2
- 4/7

69. A loaded dice has following probability distribution of occurrences

Dice value | 1 | 2 | 3 | 4 | 5 | 6 |

Probability | 1/4 | 1/8 | 1/8 | 1/8 | 1/8 | 1/4 |

If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is

- same as that of occurrence of 3, 4, 5
- same as that of occurrence of 1, 2, 5
- 1/128
- 5/8

70. Two fair dice are rolled and the sum r of the numbers turned up is considered

- Pr(r > 6) = (1/6)
- Pr(r/3 is an integer) = (5/6)
- Pr(r = 8 | r/4 is an integer) = (5/9)
- Pr(r= 6 | r/5 is an integer) = (1/18)

71. If P and Q are two random events, then the following is TRUE

- Independence of P and Q implies that probability (P ∩ Q) = 0
- Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)
- If P and Q are mutually exclusive, then they must be independent
- Probability (P ∩ Q) ≤ Probability (P)

72. A fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is

- 1/8
- 1/2
- 3/8
- 3/4

73. A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is

74. A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is

- 5/9
- 25/29
- 45/125
- 7/20

75. A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of savings account holders, who maintain an average daily balance more than Rs. 500 is

- 100
- 50
- 75
- 25

76. A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is

- 1/20
- 1/12
- 3/10
- 1/2

77. An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

- 31/32
- 16/32
- 13/32
- 1/32

78. A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing 2 washers first followed by 3 nuts and subsequently the 4 bolts is

- 1/630
- 2/315
- 1/2520
- 1/1260

79. If three coins are tossed simultaneously, the probability of getting at least one head is

- 3/8
- 1/8
- 7/8
- 1/2

80. A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?

- 1/4
- 3/8
- 1/2
- 3/4

81. A box contains 20 defective items and 80 non-defective items. If two items are selected at random without replacement, what will be the probability that both items are defective?

- 19/495
- 20/99
- 1/25
- 1/5

82. A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is

- 0.0036
- 0.1937
- 0.3874
- 0.2234

83. A single die is thrown twice. What is the probability that the sum is neither 8 nor 9?

- 1/9
- 5/36
- 1/4
- 3/4

84. From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced?

- 1/221
- 1/169
- 1/52
- 1/26

85. A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is

- 1/90
- 1/2
- 19/90
- 2/9

86. A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtaining a ‘Tail’ when the coin is tossed again is

- 0
- 1/2
- 4/5
- 1/5

87. The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is

- <50%
- 50%
- 75%
- 100%

88. In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is

- 6/32
- 3/32
- 2/32
- 1/32

89. There are two containers, with one containing 4 red and 3 green balls and the other containing 3 blue and 4 green balls. One ball is drawn at random from each container. The probability that one of the balls is red and the other is blue will be

- 1/7
- 9/49
- 12/49
- 3/7

90. A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using the public transport, further choices available are bus and metro, out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded up to two decimals) of using a car, bus and metro, respectively would be

- 0.45, 0.30 and 0.25
- 0.45, 0.25 and 0.30
- 0.45, 0.55 and 0.00
- 0.45, 0.35 and 0.20