Q121
Open questionA 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
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Probability and Statistics
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Q122
Open questionAn 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
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Q123
Open questionSuppose 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?
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Q124
Open questionA 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
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Q125
Open questionTwo 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
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Q126
Open questionA 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
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Q127
Open questionIn a service centre, cars arrive according to Poisson distribution with a mean of two cars per hour. The time of servicing a car is exponential with a mean of 15 minutes. The expected waiting time (in minute) in the queue is
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Q128
Open questionA product is an assemble of 5 different components. The product can be sequentially assembled in two different ways. If 5 components are placed in a box and these are drawn at random from the box, then probability of getting a correct sequence is
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Q129
Open questionA 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
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Q130
Open questionIf X is a continuous random variable whose probability density function is given by
{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {{\text{K}}\left( {5{\text{x}} - 2{{\text{x}}^2}} \right)}&{0 \leqslant {\text{x}} \leqslant 2} \\ 0&{{\text{otherwise}}} \end{array}} \right.
then P(x > 1) is
{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {{\text{K}}\left( {5{\text{x}} - 2{{\text{x}}^2}} \right)}&{0 \leqslant {\text{x}} \leqslant 2} \\ 0&{{\text{otherwise}}} \end{array}} \right.
then P(x > 1) is
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Q131
Open questionIn a given day in the rainy season, it may rain 70% of the time. If it rains, chances that a village fair make a loss on that day is 80%. However, if it does not rain, chances that fair will make a loss on that day is only 10%. If the fair has not made a loss on a given day in the rainy season, what is the probability that it has not rained on that day?
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Q132
Open questionTwo players, A and B, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player A starts the game, the probability that A wins the game is
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Q133
Open questionAn 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?
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?
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