Problema Solution
If the probability that the Islanders will beat the Rangers in a game is 0.31, what is the probability that the Islanders will win at most two out of seven games in a series against the Rangers? Round your answer to 7 decimal places.
Answer provided by our tutors
P(Islanders will win at most 2 out of 7 games) = P(Islanders win 0 games out of 7) + P(Islanders win 1 game out of 7) + P(Islanders win 2 games out of 7)
P(Islanders will win at most 2 out of 7 games) = C(0, 7)*(1 - 0.31)^7 + C(1, 7)*(0.31^1)(1 - 0.31)^6 + C(2, 7)(0.31^2)(1 - 0.31)^5
P(Islanders will win at most 2 out of 7 games) = (1 - 0.31)^7 + (7!/(7 - 1)!)*(0.31^1)(1 - 0.31)^6 + 7!/((7-2)!2!)(0.31^2)(1 - 0.31)^5
P(Islanders will win at most 2 out of 7 games) = (1 - 0.31)^7 + 7*(0.31^1)(1 - 0.31)^6 + 21(0.31^2)(1 - 0.31)^5
P(Islanders will win at most 2 out of 7 games) = 0.6242831