Probability and Statistics NPTEL Week 2 Assignment Answers 2023

I have provided probable answers for all 10 quiz questions for week 2’s assignment. I encourage you to utilize these hints as a guide and complete the assignment before the deadline for submission.

Probability and Statistics NPTEL Assignment – WEEK 2

Q1.Two cards are drawn successively from a pack without replacing the first. If the first card is spade, then what is the probability that the second card is also a spade?

Answer: (C) 4/17

Q2. Four of the seven balls in a box have odd numbers on them. What is the probability that all three balls picked at random, one after the other, without replacement, have odd numbers?

Answer: (B) 4/35

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Q3.Two urns contain respectively 2 white and 1 black balls, and 1 white and 5 black balls. One ball is transferred from the first to the second urn, and then a ball is drawn from the second urn. What is the probability that the ball drawn is white?

Answer: (D) 5/21

Q4.There are 2 boxes: Box-1 contains 3 silver spoons and 3 copper spoons and Box-2 contains 5 copper and 3 silver spoons. Assume that Box-1 is likely to be chosen with a probability of 2/3 and Box-2 is likely to be chosen with a probability of 1/3. A spoon is chosen at random from a box that has been randomly selected. What is the probability that it is a silver spoon?

Answer: (A) 11/24

Q5) The chance that a certain disease is diagnosed correctly is 60%. The chance that the patient will die under the treatment, after correct diagnosis is 40%; and the chance of death by wrong diagnosis is 70%. A patient who had the disease died. What is the probability that his / her disease was diagnosed correctly?

Answer: (B) 6/13

Q6.Let X be a discrete random variable with the p.m.f. as

Find P(|X|>1).

Answer: (C) 2/9

Q7.It is known that 2.5% of mobile phone chargers fail during the warranty period provided they are kept dry. The failure percentage is 5.6, if they are ever wet during the warranty period. If 91% of the chargers are kept dry and 9% are wet during warranty period, what is the probability that a phone charger fails during the warranty period?

Answer: (D) 0.0278

Q8.A random variables X has the following probability mass functions

Find P(X<3)

Answer: (C) 0.455

Q9.Suppose the probabilities of n mutually independent events are P1, P2, Pn respectively. Then what is the probability that at least one of the events will occur?

Answer: (B) 1 – (1-P1)…(1-Pn)

Q10. Some elements in a chemical laboratory are highly contaminated. A high amount of contamination in an element is likely to exist with a 0.1 probability. The levels of contamination are evaluated on four randomly chosen elements. How likely is it that at least one of them has high level of contamination?

Answer: (C) 0.6561

Disclaimer: It is imperative to note that the responses provided here are solely for educational reference purposes. This platform does not guarantee the accuracy of the answers, hence it is strongly recommended to undertake your assignments independently.

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