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Probability and Statistics NPTEL Assignment answers – Week 1

I have provided probable answers for all 10 quiz questions for week 1’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 1

Q1.In a tuition batch of two students, probability that X will pass the exam is 1/4 and that of Y is 1/2 What is the probability that neither of X and Y will pass the exam? Assume that the outcomes of exams for X and Y are independent of each other.

Answer: (B) 1/4

Q2. Two dices are tossed together. What is the probability that the product of the number is either a prime number or is divisible by 2?

Answer: (B) 8/9

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Q3.There are seven apples, five mangoes and ten guavas in a basket. Four fruits are selected at random one by one without replacement. What is the probability that first fruit drawn is a mango, second one is a guava and the third one is an apple and the fourth one is again a mango?

Answer: (D) 5/627

Q4.One ball is drawn at random from each of two baskets, where first basket contains 3 red and 5 black balls and second basket has 4 red and 7 black balls. What is the probability that both the balls are black?

Answer: (C) 35/88

Q5) A die is rolled twice independently. What is the probability that either the first throw shows a number less than or equal to 3 or the second throw shows at least 5.

Answer: (C) 2/3

Q6.From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

Answer: (D) 1/221

Q7.Let E₁, E₂, E3 be 3 independent events such that P(Ei) = 1 − 1/2i, i = 1,2,3. Then what is the probability that exactly two of the events occur?

Answer: (A) 31/64

Q8.Two independent events E and F are such that P(E∩F) =1/6 P(Eº ∩ Fº) = 1/3 and P(E)- P(F) > 0. Then P(Fº)=

Answer: (A) 2/3

Q9.A box contains 1000 light bulbs. The probability that there is at least 1 defective bulb in the box is 0.1, and the probability that there are at least 2 defective bulbs is 0.05. Find the probability that the box contains at most 1 defective bulb?

Answer: (C) 0.95

Q10. Suppose = sample space of the experiment where a three faced dice is thrown with prime numbers among numbers 1-6 as the faces. Consider
A₁ = {0,0}, A₂ = {0, 0, {2,3}, {1,5}, {1,2,3,5}}, A3 = {0, 0, {1,2,3}, {4,5,6}}, A4 = {n, p, {2,5}, {3}}. Then which of the following forms a sigma field?

Answer: (C) A1 AND A4

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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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