A basketball promoter nas decided to hold a holiday tourname

A basketball promoter nas decided to hold a holiday tournament at the University of Kentucky involving eight highly ranked college teams. the promoter hops that Kentucky and Louisville eventually play each other in the final game so that rights can be sold for a handsome profit. Because Louisville and Kentucky are in opposite halves of the draw, they cannot Play each other before the final game. To reach the final a team must win its two preceding games. Louisville reaches the finals. Kentucky reaches the finals. Kentucky plays Louisville in the finals. Neither Kentucky nor Louisville plays in the finals.

Solution

a)

P(L gets win, win) = 0.7*0.4 = 0.28 [ANSWER]

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b)

P(K gets win, win) = 0.8*0.5 = 0.40 [ANSWER]

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c)

Hence, the probability that they both play in the finals is

P(L vs K) = 0.28*0.40 = 0.112 [ANSWER]

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c)

P(neither play) = 1 - P(at least one fo them play)

= 1 - (P(L plays) + P(K plays) - P(both play))

= 1 - (0.28 + 0.40 - 0.112)

= 0.432 [ANSWER]