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
Q6. Let X be a discrete random variable with the p.m.f. as X=x -2 -1 0 1 2 p(x) 1/9 2/9 3/9 2/9 1/9 Find 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 5 P(X=x) 0 2k 3k 2k2 4k 9k2+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
