# Probability And Statistics | Week 1

## Probability And Statistics Week 1 Answers

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, 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?
(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
(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 A3
(B) A₁ and A₂
(C) A₁ and A4
(D) A₁, A2, A3 and A4