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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.

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?

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?

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?

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.

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

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?

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)=

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?

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?

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