Question

if the probability that the islanders will beat the rangers in a game is 0.44,what is the probability that the islanders will win exactly one out of four games in a series against the rangers? ​

Answer 1

Answer:

30.91% probability that the islanders will win exactly one out of four games in a series against the rangers

Step-by-step explanation:

For each game, there are only two possible outcomes. Either the Islanders win, or they do not. The probability of the Islanders winning a game is independent of other games. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability that the islanders will beat the rangers in a game is 0.44

This means that $p = 0.44$

What is the probability that the islanders will win exactly one out of four games in a series against the rangers? ​

This is P(X = 1) when n = 4. Then

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{4,1}.(0.44)^{1}.(0.56)^{3} = 0.3091$

30.91% probability that the islanders will win exactly one out of four games in a series against the rangers