# Probability And Statistics | Week 1

## Probability And Statistics Week 1 Answers

**Link : Probability And Statistics (nptel.ac.in)**

## Checkout Answers in comments also of your fellow-mates!

**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.**

(A) 1/6

(B) 1/4

(C) 7/12

(D) 5/12

**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?**

(A) 3/36**(B) 8/9**

(C) 7/36

(D) 5/36

**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?**

(A) 10/627

(B) 5/132

(C) 5/144**(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?**

(A) 7/30

(B) 7/60**(C) 35/88**

(D) 3/22

**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.**

(A) 5/9

(B) 7/3**(C) 2/3**

(D) 1/2

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

(A) 1/3

(B) 1/15

(C) 25/57**(D) 1/221**

**Q7) Let E₁, E₂, E _{3} be 3 independent events such that P(E_{i}) = 1 − 1/2^{i}, i = 1,2,3. Then what is the probability that exactly two of the events occur?**

**(A) 31/64**

(B) 10/64

(C) 3/64

(D) 7/64

**Q8) Two independent events E and F are such that P(E ∩** **F) =1/6 , P(E’ ∩ F’) = 1/3 and P(E)- P(F) > 0. Then P(F’)=****(A) 2/3**

(B) 1/2

(C) 1/3

(D) 1/6

**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?**

(A) 0.25

(B) 0.48**(C) 0.95** ** – answerd by garima (comments)**

(D) 0.60

**Q10) Suppose Ω** = **sample space of the experiment where a three faced dice is thrown with prime numbers among numbers 1-6 as the faces. Consider**

(A) A₁, A₂ and A_{3} ** **

(B) A₁ and A₂ **(C) A₁ and A _{4}**

(D) A₁, A

_{2}, A

_{3}and A

_{4}

Answer 9. (C) 0.95

Explanation – We can use complement rule for the probability of an event A to find the probability of its complement event, i.e. the event that A does not occur. The probability of at most 1 defective bulb is the complement of the event of having at least 2 defective bulbs, so it is given by:

P(at most 1 defective bulb) = 1 – P(at least 2 defective bulbs) = 1 – 0.05 = 0.95