21. 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
22. 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
23. 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?
24. 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
25. 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
26. 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
27. In 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
28. A 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
29. 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
30. If 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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