Every years two teams, Unggul and Bestari meets each other in a debate competition. Past results show that in years when Unggul win, the probability of them winning the next year is 0.6 and in years when Bestari win, the probability of them winning the next year is 0.5. it is not possible for the competition to result in a tie. Unggul won the competition in 2011. a. Construct a probability tree diagram for the three years up to 2014. b. Find the probability that Bestari will win in 2014. c. If Bestari wins in 2014, find the probability that it will be their first win for at least three years.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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25 Every years two teams, Unggul and Bestari meets each other in a debate competition. Past results show
that in years when Unggul win, the probability of them winning the next year is 0.6 and in years when
Bestari win, the probability of them winning the next year is 0.5. it is not possible for the competition
to result in a tie. Unggul won the competition in 2011.
a. Construct a probability tree diagram for the three years up to 2014.
b. Find the probability that Bestari will win in 2014.
c. If Bestari wins in 2014, find the probability that it will be their first win for at least three
years.
d. Assuming that Bestari wins in 2014, find the smallest value of n such that the probability of
Unggul wins the debate competition for n consecutive years after 2014 is less than 0.05.
Transcribed Image Text:25 Every years two teams, Unggul and Bestari meets each other in a debate competition. Past results show that in years when Unggul win, the probability of them winning the next year is 0.6 and in years when Bestari win, the probability of them winning the next year is 0.5. it is not possible for the competition to result in a tie. Unggul won the competition in 2011. a. Construct a probability tree diagram for the three years up to 2014. b. Find the probability that Bestari will win in 2014. c. If Bestari wins in 2014, find the probability that it will be their first win for at least three years. d. Assuming that Bestari wins in 2014, find the smallest value of n such that the probability of Unggul wins the debate competition for n consecutive years after 2014 is less than 0.05.
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