tutorial2 - If a student correctly answers the rst...

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Stat 211 - Tutorial 2 1. You are given that A and B are independent events. Additionally, P ( A ) = 7 16 and P ( B ) = 5 16 .Find P ( A B ) and P ( A B ) . 2. You are given that A and B are mutually exclusive events. Additionally, P ( A ) = 7 16 and P ( B ) = 5 16 .Find P ( A B ) and P ( A B ) . 3. ABC Ltd. has 3 machines A , B and C . In any given week, the probability that a machine breaks down is 0.04 for A , 0.02 for B and 0.01 for C , with breakdowns being independent of each other. On a randomly chosen week, find the probability that (a) at least one of the machines break down. (b) machine C breaks down, given that exactly one machine breaks down. 4. Three people A , B and C are playing cards, each being equally likely to win the game. (a) In two consecutive games, i. find the probability that both A and B each win one game. ii. given that A wins at least one game, find the probability that C wins the second game. (b) Suppose instead that the probability that C wins a game is 5 / 7 , and that A and B are equally likely to win a game. Repeat part a). 5. In a final exam, the probability that the first question is answered correctly is 0.8.
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Unformatted text preview: If a student correctly answers the rst question, the probability that she correctly answers the second question is 0.6. If she answered the rst question wrongly, then the probability she correctly answers the second question is 0.4. (a) Find the probability that she answers the second question correctly. (b) Given that she answers the second question correctly, nd the probability that she answered the rst question correctly. 6. 95% of parts produced by a machine in a day are within the required specication. In a given day, ten parts are randomly selected. Find the probability that (a) exactly 1 part is not within specication. (b) at least one part is within specication. (c) Let X denote the number of parts in the sample of 10 that are within specica-tion. Find E ( X ) , E (2 X + 10) , V ar ( X ) and V ar (2 X + 10) . 1...
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