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If the probability that the Islanders will beat the Rangers in a game is 5/9, what is the probability that the Islanders will win exactly three out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.

Sagot :

mhanifa

Answer:

  • 0.235

Step-by-step explanation:

Probability of win is:

  • p(w) = 5/9 = 0.555

Probability of loss is:

  • p(l) = 1 - p(w) = 1 - 0.555 = 0.445

Combinations of 3 wins out of 7 games is:

  • 3C7 = 7!/3!4! = 7*6*5/2*3 = 35

Required probability:

  • P = 35*(0.555)³(0.445)⁴ = 0.235 (rounded)
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