GTU 3130006 Probability and Statistics (PS) Summer 2026 Paper Solution & PDF

A committee of 4 people is to be appointed from 3 teachers, 4 health officers, 2 security personnel and 1 chartered accountant. Find the probability of forming the committee so that the chartered accountant is mandatorily present in the committee.

A student doing his online homework on a regular basis has a chance of 83 percent to get a good grade; but the chance drops to 58 percent if he doesn’t do the homework regularly. The student figures out that he has only 69 percent chance of doing the homework regularly. What is his chance of not getting a good grade in the course?

From a vessel containing 3 white and 5 black balls, 4 balls are transferred into an empty vessel. From this new vessel, a ball is drawn and is found to be white. What is the probability that out of the 4 balls transferred, 3 are white and 1 is black?

Two variates have the regression lines as x + 4y + 3 = 0 and 4x + 9y + 5 = 0. Find the correlation coefficient.

If 𝑝(𝑥) = 𝑥/15; 𝑥 = 1, 2, 3, 4, 5 = 0, otherwise

A car hire firm has two cars, which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson distribution with mean 1.5. Calculate the proportion of days on which (i) neither car is used (ii) some demand is refused.

A random variable X with unknown probability distribution has a mean 8 and standard deviation 3. Evaluate the bounds on P (- 4 < X < 20).

x 61 26 7 2.6 y 350 400 500 600

Find the coefficient of variation of the marks obtained by the students of a college: Marks : 20-30 30-40 40-50 50-60 60-70 No. of Students : 2 35 46

The arrival rate of cars at a gas station is 40 customers per hour. What is the probability of having no arrival of cars in a 5 minute interval?

The standard deviations calculated from two random samples of sizes 9 and 13 are 2.1 and 1.8 respectively. May the samples be regarded as drawn from normal populations with the same standard deviation? (Test at 5% significance level)

In a flu epidemic, 500 persons contracted the disease. 200 receives no serum treatment and of these 75 died. Of those who did receive serum treatment, 65 died. Was the serum treatment effective? Use test at 1% significance level.

The mean weekly sales of soap bars was 146.3 bars per store. After an advertising campaign, the mean weekly sales in 22 stores for a typical week increased to 153.7 with standard deviation of 17.2. Was the advertising campaign successful? ( Test at 5% level)

A test is carried out to check the efficiency of both the factories ascertaining the variability of the life of the bulbs produced by each factory. The results are as follows: Factory A Factory B Standard deviation of lifetime (hours) 240 220 No. of bulbs in sample 100 200 Determine whether the difference between the variability of life of light bulbs from the two factories is significant (Test at 1% level).

In his experiments on pea-breeding, Mendel obtained the following frequencies of seeds: Class Observed Frequency Round and yellow 315 Wrinkled and yellow 101 Round and green 108 Wrinkled and green 32 Total 556 Theory predicts that the frequencies should be in the proportions 9 : 3 : 3 : 1. Use test to examine the correspondence between theory and observations at 5% significance level.