Probability MCQ

91. There are 25 calculators in a box. Two of them are defective. Suppose 5 calculators are randomly picked for inspection (i.e., each has the same chance of being selected), what is the probability that only one of the defective calculators will be included in the inspection?

1. 1/5
2. 1/4
3. 1/3
4. 1/2

92. A hydraulic structure has four gates which operate independently. The probability of failure of each gate is 0.2. Given that gate 1 has failed, the probability that both gates 2 and 3 will fail is

1. 0.200
2. 0.240
3. 0.008
4. 0.040

93. A box contains 10 screws, 3 of which are defective. Two screws are drawn at random with replacement. The probability that none of the two screws is defective will be

1. 100%
2. 50%
3. 49%
4. None of these

94. Suppose p is the number of cars per minute passing through a certain road junction between 5 PM, and p has Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?

1. 8/(2e³)
2. 9/(2e³)
3. 26/(2e³)
4. 17/(2e³)

95. Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2 or 3 the die is rolled a second time. What is the probability that the sum of total values that turn up is at least 6?

1. 5/12
2. 10/21
3. 1/6
4. 2/3

96. Consider the finite sequence of random values X= [x₁, x₂, ….., x_n]. Let μ_x be the mean and σ_x, be the standard deviation of X. Let another finite sequence Y of equal length be derived from this as y_i = a*x_i, + b, where a and b are positive constant. Let μ_y be the mean and σ_y be the standard deviation of this sequence. Which one of the following statements INCORRECT?

1. Index position of mode of X in X is the same as the index position of mode of Y in Y.
2. Index position of median of X in X is the same as the index position of median of Y in Y
3. μ_y = aμ_x + b
4. σ_y = aσ_x + b

97. A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?

1. 1/5
2. 4/25
3. 1.4
4. 2/5

98. Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company, therefore, subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?

1. pq + (1- p) (1- q)
2. (1-q)p
3. (1-p)q
4. pq

99. If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

1. 1/4
2. 1/3
3. 2/3
4. 1/2

100. An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even-numbered face is the same. If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3?

1. 0.453
2. 0.468
3. 0.485
4. 0.492

101. Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that she studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?

1. 0.24
2. 0.36
3. 0.4
4. 0.6

102. Suppose we uniformly and randomly select a permutation from the 20! permutations of 1, 2, 3, ……, 20. What is the probability that 2 appears at an earlier position that any other even number in the selected permutation?

1. 1/2
2. 1/10
3. 9!/20!
4. None of these

103. Two n bit binary strings, S1 and S2 are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to d is

1. ⁿC_d/2ⁿ
2. ⁿC_d/2^d
3. d/2ⁿ
4. 1/2^d

104. If a fair coin is tossed four times. What is the probability that two heads and two tails will result?

1. 3/8
2. 1/2
3. 3/4
4. 5/8

105. Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = 1/2, the values of P(A/B) and P(B/A) respectively are

1. 1/4, 1/2
2. 1/2, 1/4
3. 1/2, 1
4. 1, 1/2

106. A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is

1. 2/6
2. 2/36
3. 1/2
4. 5/12

107. A fair coin is tossed independently four times. The probability of the event ”the number of times heads show up is more than the number of times tails show up” is

1. 1/16
2. 1/8
3. 1/4
4. 5/16

108. A fair coin is tossed 10 times. What is the probability that only the first two tosses will yield heads?

1. (1/2)²
2. ¹⁰C₂(1/2)²
3. (1/2)¹⁰
4. ¹⁰C₂(1/2)¹⁰

109. An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is

1. 0.18
2. 0.5
3. 0.12
4. 0.06

110. Three companies X, Yand Z supply computers to a university. The percentage of computers supplied by them and the probability of those being defective are tabulated below:

Company	% of computer	Probability of being supplied defective
X	60%	0.01
Y	30%	0.02
Z	10%	0.03

Given that a computer is defective, the probability that it was supplied by Y is

1. 0.2
2. 0.1
3. 0.3
4. 0.4

111. A fair dice is rolled twice. The probability that an odd number will follow an even number is

1. 1/2
2. 1/6
3. 1/3
4. 1/4