In a shotgun seminar,the topic is announced one week in advance, but the speaker

Question

In a shotgun seminar,the topic is announced one week in advance, but the speaker
is randomly chosen when the seminar begins. Suppose that you attend12 seminars with 9 other
participants.
(a) What is the expected number of times you will be selected asspeaker?
(b) What is the probability that you will be selected twice?
(c) Suppose that the 10 participants are divided into ve teams oftwo for preparation. What is
the probability that your team (i.e., either you or your partner)will be selected twice? Thanks a lot. In a shotgun seminar,the topic is announced one week in advance, but the speaker
is randomly chosen when the seminar begins. Suppose that you attend12 seminars with 9 other
participants.
(a) What is the expected number of times you will be selected asspeaker?
(b) What is the probability that you will be selected twice?
(c) Suppose that the 10 participants are divided into ve teams oftwo for preparation. What is
the probability that your team (i.e., either you or your partner)will be selected twice? Thanks a lot. Thanks a lot.

Explanation / Answer

Binomial distribution :n=12; p=1/9 a) Expected times chosen is the mean np=4/3 b) P(chosentwice)=C(12,2)(1/9)2(8/9)10=.251 c)P(group chosen)=1/5 P(group chosen twice)=C(12,2)(1/5)2(4/5)10=.283 c)P(group chosen)=1/5 P(group chosen twice)=C(12,2)(1/5)2(4/5)10=.283

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