Individual A has a circle of five close friends (B, C, D,E, and F). A has heard a certain rumor from outside thecircle and has invited the five friends to a party to circulatethe rumor. To begin, A selects one of the five atrandom and tells the rumor to the chosen individual.That individual then selects at random one of the fourremaining individuals and repeats the rumor. Continuing,a new individual is selected from those not already havingheard the rumor by the individual who has just heardit, until everyone has been told.a. What is the probability that the rumor is repeated inthe order B, C, D, E, and F?b. What is the probability that F is the third person atthe party to be told the rumor?c. What is the probability that F is the last person tohear the rumor?d. If at each stage the person who currently “has” therumor does not know who has already heard it andselects the next recipient at random from all fivepossible individuals, what is the probability that Fhas still not heard the rumor after it has been told tentimes at the party?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 74E: Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is...
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Individual A has a circle of five close friends (B, C, D,
E, and F). A has heard a certain 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 at random one of the four
remaining 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
the order B, C, D, E, and F?
b. What is the probability that F is the third person at
the party to be told 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 the next recipient 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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