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Probability practice solutions

If a and b are disjoint events with p a 020 and p b

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15. If  A  and  B  are disjoint events, with  P ( A ) = 0.20 and  P ( B ) = 0.30, then  P ( A  and  B ) is: a. 0.50 b. 0.10 c. 0.00 d. 0.06 ANSWER: c 16. If event  A  does not occur, then its complement  C A  will also not occur. ANSWER:  F 17. Marginal probability is the probability that a given event will occur, with no other events  taken into consideration.  ANSWER: T 18. Conditional probability is the probability that an event will occur, given that another  event will also occur. ANSWER:  T A construction company has submitted bids on two separate state contracts,  A  and  B . The  company feels that it has a 60% chance of winning contract   A , and a 50% chance of  winning contract   B . Furthermore, the company believes that it has an 80% chance of  winning contract  A  given that it wins contract  B . 1 st  step to solving this is to write out what they give you in proper notation: P(A) = .60, P(B) = .50, P(A|B) = .80 19. What is the probability that the company will win both contracts? ANSWER: “both contracts” means we want P(A and B) P(A and B) = P(A|B)P(B) = (.80)(.50) = .40 20.   What is the probability that the company will win at least one of the two contracts? ANSWER: “at least one of the two” means winning: A, or B or both A and B. This implies that  we want P(A or B). P(A or B) = P(A) + P(B) – P(A and B) = (.60) + (.50) – (.40) = .70 21. If the company wins contract  B , what is the probability that it will not win contract  A ? 3
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ANSWER: We want the conditional probability: P(A C |B) P(A C |B) = 1 – P(A|B) = 1 - .80 = .20 22. What is the probability that the company will win at most one of the two  contracts? ANSWER: The possible outcomes are: (A C  and B C ), (A and B C ), (A C  and B), (A and B) Since these are the only outcomes, the probabilities of each must sum to 1. “At most one of the two” means we want the probability of the first 3 outcomes  listed – since we can have all the outcomes happen except winning both contracts.  We can use the complement rule to find it, using the answer to question 19: P(at most 1 of the 2) = 1 – P(A and B) = 1 - .40 = .60 23. What is the probability that the company will win neither contract? ANSWER: We can again use the complement rule for this.   Looking at the list of possible  outcomes from the solution to #22, the complement to the company winning neither,  is that the company wins at least one of the two contracts.  Thus, we can use our  answer to question 20:  P(A C  and B C ) = 1 – P(A or B) = 1 - .70 = .30 24.
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