11. A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing 2 washers first followed by 3 nuts and
subsequently the 4 bolts is
12. An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches -0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability, The sum total of the expected marks obtained by all these students is
13. 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
For f(x) to be valid probability density function, the value of h is
14. 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
15. 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?
16. Two cards are drawn at random in succession with replacement from a deck of 52 well shuffled card. Probability of getting both aces is
17. 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
18. The function p(x) is given by $${\text{p}}\left( {\text{x}} \right) = \frac{{\text{A}}}{{{{\text{x}}^\mu }}}$$ where A and μ are constants with μ > 1 and 1 ≤ x < $$\infty $$ and p(x) = 0 for $$ - \infty $$ < x < 1. For p(x) to be a probability density function, the value of A should be equal to
19. A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?
20. 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
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