SOLUTION: Four runners are competing for a gold medal in 400 meters hurdles. Runner B is twice as likely to win as A. Runner C is twice as likely to win as B and Runner D is twice as likely

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Question 898152: Four runners are competing for a gold medal in 400 meters hurdles. Runner B is twice as likely to win as A. Runner C is twice as likely to win as B and Runner D is twice as likely to win as C. Determine the probability of each runner winning. What is the probability that runner C and D will win the race?
Answer by stanbon(75887) (Show Source):
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Four runners are competing for a gold medal in 400 meters hurdles. Runner B is twice as likely to win as A. Runner C is twice as likely to win as B and Runner D is twice as likely to win as C. Determine the probability of each runner winning. What is the probability that runner C and D will win the race?
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P(A wins) = x
P(B wins) = 2x
P(C wins) = 4x
P(D wins) = 8x
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Solve for x::
x + 2x + 4x + 8x = 1
15x = 1
x = 1/15 - P(A wins)
2x = 2/15 = P(B wins)
4x = 4/15 = P(C wins)
8x = 8/15 = P(E wins)
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P(C AND D win) = ?
Note: They cannot both win.
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Cheers,
Stan H.