Mathematics, 14.03.2020 04:13 dvandebrake2002

Individual A has a circle of five close friends (B, C, D, E and F). A has heard a rumor from outside the circle and has invited the five friends to a party to circulate the rumor. To begin, A selects one of the five at random and tells the rumor to the chosen individual. That individual then selects one of the remaining four individuals and repeats the rumor. Continuing, a new individual is selected from those not already having heard the rumor by the individual who has just heard it, until everyone has been told.

a. What is the probability that the rumor is repeated in order B, C, D, E and F?

b. What is the probability that F is the third person to hear the rumor?

c. What is the probability that F is the last person to hear the rumor?

d. If at each stage the person who currently "has" the rumor does not know who has already heard it and selects at random from all five possible individuals, what is the probability that F has still not heard the rumor after it has been told ten times at the party?

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Individual A has a circle of five close friends (B, C, D, E and F). A has heard a rumor from outside...