GTU 3130006 Probability and Statistics (PS) Summer 2025 Question Paper & PDF

A coin is tossed three times. What is the probability of getting exactly two heads?

x 1 2 3 4 5 y 2 5 10 17 26

Does there exists a binomial distribution for which variance is greater than mean?

A biased coin returns head 10% of times. Find the probability of getting exactly 2 heads in 10 trials using binomial distribution.

A factory has three machines A, B, and C producing 20%, 30%, and 50% of the total items, respectively. The probabilities of producing a defective item are 1%, 2%, and 3% for A, B, and C, respectively. If an item is defective, what is the probability that it was produced by machine B?

x 1 2 3 4 5 y 2 1 5 4

x 1 2 3 4 5 6 7 y

In a sample of 500 bulbs 20 are found defective. The company claims that only 2% bulbs are defective. Test the reality of claim at 5% level of significance.

Test whether the following samples could have been drawn from population with same SD. Sample A Sample B Size 100 200 SD

Two cards are chosen randomly from deck. What is probability that (a) both are ace? (b) both are black? (c) none is ace (d) none is black

Weight of 1000 experimental animals is normally distributed with mean 235 grams and standard deviation 35. How many animals weigh (a) below 172 grams (b) above 312 grams (c) between 172 to 312 grams. [P(Z=1.8)=0.4641,P(Z=2.2)=0.4841]