21 if the company wins contract b what is the

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21. If the company wins contract  B , what is the probability that it will not win contract  A ? 22. What is the probability that the company will win at most one of the two  contracts? 23. What is the probability that the company will win neither contract? 3
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24. A pharmaceutical firm has discovered a new diagnostic test for a certain disease that has  infected 1% of the population. The firm has announced that 95% of those infected will show a  positive test result, while 98% of those not infected will show a negative test result. What  proportion of test results are correct? A Ph.D. graduate has applied for a job with two universities:  A  and  B . The graduate feels  that she has a 60% chance of receiving an offer from university  A  and a 50% chance of  receiving an offer from university  B . If she receives an offer from university  B , she believes  that she has an 80% chance of receiving an offer from university  A . 25. What is the probability that both universities will make her an offer? 26. What is the probability that at least one university will make her an offer? 27. If she receives an offer from university  B , what is the probability that she will not receive an  offer from university  A ? 28. At the beginning of each year, an investment newsletter predicts whether or not the stock  market will rise over the coming year. Historical evidence reveals that there is a 75% chance that  the stock market will rise in any given year. The newsletter has predicted a rise for 80% of the  years when the market actually rose, and has predicted a rise for 40% of the years when the  market fell. Find the probability that the newsletter’s prediction for next year will be correct.
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