Probability and statistics questions with answers
71 multiple-choice questions. Open any question for its answer and explanation.
- 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?
- The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is
- X and Y are two independent random variables with variances 1 and 2, respectively. Let Z = X - Y. The variance of Z is
- A random variable is uniformly distributed over the interval 2 to 10. Its variance will be
- A box has 8 red balls and 8 green balls. Two balls are drawn randomly in succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is
- The diameters of 10000 ball bearings were measured. The mean diameter and standard deviation were found to be 10 mm and 0.05 mm respectively. Assuming Gaussian distribution of measurements, it can be expected that the number of measurement more than 10.15 mm will be
- A continuous random variable X has a probability density f(x) = e-x, 0 < x < $$\infty $$ . Then P{X > 1} is
- Two white and two black balls, kept in two bins are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a white face picked? A. B. C. D.
- 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
- Considers a sequence of tossing of a fair coin where the out comes of tosses are independent. The probability of getting the head for the third time in the fifth toss is
- 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?
- A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- In 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?
- 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?