GATE CE Probability and Statistics PYQs & Answers

Questions 1–10 of 29. Imported answers require independent review unless marked reviewed.

Bag I contains 4 white and 6 black balls. Bag II contains 4 white and 3 black balls. One ball is drawn at random from any one of the two bags and it is found to be a black ball. The probability that the black ball was drawn from Bag I is ______ (rounded off to two decimal places).

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The age (in years) of a population is normally distributed with a mean of 36 and standard deviation of 12. The height (in cm) of the same population is also normally distributed with a mean of 160 and standard deviation of 10.

If the probability of age greater than 50 years is equal to the probability of height greater than h, the value of h (in cm) is ______ (rounded off to two decimal places).

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is a random variable that can take any one of the values 0, 1, 7, 11, and 12. The probability mass function for

Then, the variance of

Your answerChoose one option.

20.81

28.40

31.70

10.89

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Given that A and B are not null sets, which of the following statements regarding probability is/are CORRECT?

Your answerSelect all correct options. You can choose more than one.

P(A∩B) = P(A) P(B), if A and B are mutually exclusive.

Conditional probability, P(A|B) = 1 if B ⊂ A.

P(A∪B) = P(A) + P(B), if A and B are mutually exclusive.

P(A∩B) = 0, if A and B are independent.

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Consider a discrete random variable

whose probabilities are given below. The standard deviation of the random variable is _____ (round off to one decimal place).

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A one-way, single lane road has traffic that consists of 30% trucks and 70% cars. The speed of trucks (in km/h) is a uniform random variable on the interval (30, 60), and the speed of cars (in km/h) is a uniform random variable on the interval (40, 80). The speed limit on the road is 50 km/h. The percentage of vehicles that exceed the speed limit is __________ (rounded off to 1 decimal place).

Note: X is a uniform random variable on the interval (α, β), if its probability density function is given by

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The probability that a student passes only in Mathematics is

. The probability that the student passes only in English is

. The probability that the student passes in both of these subjects is

. The probability that the student will pass in at least one of these two subjects is

Your answerChoose one option.

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In a sample of 100 heart patients, each patient has 80% chance of having a heart attack without medicine X. It is clinically known that medicine X reduces the probability of having a heart attack by 50%. Medicine X is taken by 50 of these 100 patients. The probability that a randomly selected patient, out of the 100 patients, takes medicine X and has a heart attack is

Your answerChoose one option.

40%

60%

20%

30%

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The return period of a large earthquake for a given region is 200 years. Assuming that earthquake occurrence follows Poisson’s distribution, the probability that it will be exceeded at least once in 50 years is __________ % (rounded off to the nearest integer).

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Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function),

, of a variable

Diagram for Civil Engineering question 7

Your answerChoose one option.

mean = median ≠ mode

mean = median = mode

mean ≠ median = mode

mean ≠ mode = median

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GATE CE Probability and Statistics PYQs

How to practice Probability and Statistics

Question 26

Question 47

Question 14

Question 22

Question 51

Question 63

Question 13

Question 36

Question 47

Question 7