# Probability And Statistics | Week 2

**Course Name: Probability And Statistics**

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**These are Probability And Statistics Week 2 Assignment 2 Answers**

**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?**

(A) 13/51

(B) 12/13

(C) 4/17

(D) 3/17

**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?**

(A) 24/343

(B) 4/35

(C) 2/7

(D) 64/343

**Answer: (B) 4/35**

**These are Probability And Statistics Week 2 Assignment 2 Answers**

**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?**

(A) 1/21

(B) 1/3

(C) 4/21

(D) 5/21

**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 and Box-2 is likely to be chosen with a probability of A spoon is chosen at random from a box that has been randomly selected. What is the probability that it is a silver spoon?**

(A) 11/24

(B) 1/3

(C) 1/8

(D) 5/24

**Answer: (A) 11/24**

**These are Probability And Statistics Week 2 Assignment 2 Answers**

**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?**

(A) 24/25

(B) 6/13

(C) 3/14

(D) 1/6

**Answer: (B) 6/13**

**Q6. Let X be a discrete random variable with the p.m.f. asX=x -2 -1 0 1 2p(x) 1/9 2/9 3/9 2/9 1/9Find P(|X|>1).**

(A) 1/3

(B) 7/9

(C) 2/9

(D) 8/9

**Answer: (C) 2/9**

**These are Probability And Statistics Week 2 Assignment 2 Answers**

**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?**

(A) 0.3321

(B) 0.4392

(C) 0.0391

(D) 0.0278

**Answer: (D) 0.0278**

**Q8. A random variables X has the following probability mass functions****X 0 1 2 3 4 5P(X=x) 0 2k 3k 2k ^{2} 4k 9k^{2}+k**

**Find P(X < 3).**

(A) 0.622

(B) 0.378

(C) 0.455

(D) 0.471

**Answer: (C) 0.455**

**These are Probability And Statistics Week 2 Assignment 2 Answers**

**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?**

(A) 1- P₁ — Pn

(B) 1 (1-P₁) … (1-P)

(C) (1P₁) … (1-Pn)

(D) P₁ — Pn

**Answer: (B) 1 (1-P₁) … (1-P)**

**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 a high level of contamination?**

(A) 0.2048

(B) 0.4096

(C) 0.6561

(D) 0.7408

**Answer: (C) 0.6561**

**These are Probability And Statistics Week 2 Assignment 2 Answers**

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**These are Probability And Statistics Week 2 Assignment 2 Answers**