Problem 2 (5 points) a. (1 point) Consider a carton of twelve eggs, of which thr

Question

Problem 2 (5 points) a. (1 point) Consider a carton of twelve eggs, of which three are rotten. Suppose we randomly select five eggs. Compute the probability that there is at least one rotten egg among the selected eggs. Explain. b. (2 points) Suppose a student must take an oral exam on three of ten possible topics. She has studied eight of these topics, but did not have time to study the final two topics. On the day of the exam, she must randomly select three of ten cards (one for each possible topic) and answer questions on those three topics. Determine the probability that she will be examined on 0, 1, 2, or 3 topics that she has studied for (i.e., compute the four specified probabilities). Explain c. Suppose a stockbroker has recommended eight stocks to a client and that five of the recommended stocks will increase in value over the next year

Explanation / Answer

2 a)

Total eggs 12

Rotten 3, good = 9

Probability that atleast one egg will be rotten out of 5 = 1 – probability all eggs are good

= 1 – 9C5/12C5

= 1 – 0.02 = 0.98

2 b)

Total topics =10

Prepared = 8, not prepared = 2

To select =3

P(she will be examined on 0 prepared topic) = 0 (as out of 3 atleast one will be prepared as unprepared topics =2)

P(she will be examined on 1 prepared topic) = 1 prepared 2 unprepared

= 8C1*2C2 / 10C3 = 0.07

P(she will be examined on 2 prepared topics) = 2 prepared 1 unprepared

= 8C2*2C1 / 10C3 = 0.47

P(she will be examined on 3 prepared topics) = 3 prepared 0 unprepared

= 8C3*2C0 / 10C3 = 0.47

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