Probability and statistics
Guiding State PSC aspirants since 2016 50,000+ students · 1,000+ final selections Exam Calendar Results Call 9116926003
pscnotes
EN हिं
Pick your state

Probability and statistics questions with answers

71 multiple-choice questions. Open any question for its answer and explanation.

  1. The graph of a function f(x) is shown in the figure. For f(x) to be valid probability density function, the value of h is
  2. A sample of 15 data is as follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is
  3. What is the probability that at most 5 defective fuses will be found in a box of 200 fuses, if 2% of such fuses are defective?
  4. Two cards are drawn at random in succession with replacement from a deck of 52 well shuffled card. Probability of getting both aces is
  5. 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
  6. A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?
  7. The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is
  8. 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
  9. Two fair dice are rolled and the sum r of the numbers turned up is considered
  10. Two coins R and S are tossed. The 4 joint events HRHS, TRTS, HRTS, TRHS have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T represents tail. Which one of the following is TRUE?
  11. If {x} is a continuous, real valued random variable defined over the interval (-$$\infty $$, +$$\infty $$) and its occurrence is defined by the density function given as: $${\text{f}}\left( {\text{x}} \right) = \frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}$$ where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral $$\int_{ - \infty }^{\text{a}} {\frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}{\text{dx}}} $$
  12. Type II error in hypothesis testing is
  13. A random variable X has a probability density function, \[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {{\text{k}}{{\text{x}}^{\text{n}}}{{\text{e}}^{ - {\text{x}}}};}&{{\text{x}} \geqslant {\text{0}}} \\ {0;}&{{\text{otherwise}}} \end{array}} \right.\] (n is an integer) with mean 3. The values of {k, n} are
  14. A probability density function is of the form $${\text{p}}\left( {\text{x}} \right) = {\text{K}}{{\text{e}}^{ - \alpha \left| x \right|}},\,{\text{x}} \in \left( { - \infty ,\,\infty } \right).$$ The value of K is
  15. 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?
  16. A class of first year B. Tech. students is composed of four batches A, B, C and D, each consisting of 30 students. It is found that the sessional marks of students in Engineering Drawing in batch Chave a mean of 6.6 and standard deviation of 2.3. The mean and standard deviation of the marks for the entire class are 5.5 and 4.2, respectively. It is decided by the course instructor to normalize the marks of the students of all batches to have the same mean and standard deviation as that of the entire class. Due to this, the marks of a student in batch C are changed from 8.5 to
  17. Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is
  18. A committee of 4 is to be formed from among 4 girls and 5 boys. What is the probability that the committee will have number of boys less than number of girls?
  19. 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?
  20. A probability distribution with right skew is shown in the figure. The correct statement for the probability distribution is
  21. Two bags A and B have equal number of bails. Bag A has 20% red balls and 80% green bails. Bag B has 30% red bails. 60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red?
  22. If the standard deviation of the spot speed of vehicles in a highway is 8.8 kmph and the mean speed of the vehicles is 33 kmph, the coefficient of variation in speed is
  23. Which one of the following statements is NOT true?
  24. In a game, two players X and Y are tossing a coin alternately. Whoever gets a 'head' first, wins the game and the game is terminated. Find the chance that player X will win the game if he starts?
  25. A loaded dice has following probability distribution of occurrences Dice Value 1 2 3 4 5 6 Probability $$\frac{1}{4}$$ $$\frac{1}{8}$$ $$\frac{1}{8}$$ $$\frac{1}{8}$$ $$\frac{1}{8}$$ $$\frac{1}{4}$$ If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is