If the probability that the Islanders will beat the Rangers in a game is 5/6, what is the probability that the Islanders will win exactly five out of seven games in a series against the Rangers?

0.234

Step-by-step explanation:

Given that:

Proportion, (p) ; Islanders beat rangers = 5/6 = 0.8333

Probability that islander win exactly 5 out of 7 games

1 - p = 0.1667

Usingbthe binomial distribution formula :

P(x =x) = nCx * p^n * (1 - p)^(n - r)

P(x = 5) = 7C5 * 0.833^5 * 0.1667^2

P(x = 5) = 21 * 0.833^5 * 0.1667^2

P(x = 5) = 0.23405369484362783281917

P(x = 5) = 0.234

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2