Question

If the probability that the Islanders will beat the Rangers in a game is 2/7, what is the probability that the Islanders will win exactly zero out of six games in a series against the Rangers? Round your answer to the nearest thousandth.

Answer 1

0.1328 is the probability that the Islanders will win exactly zero out of six games in a series against the Rangers.

Step-by-step explanation:

Given data is that probability the islanders will beat the rangers in a game is $\frac{2}{7}$.

So, probability that the islanders will not beat the rangers in the game is = $1-\frac{2}{7}=\frac{5}{7}$

Let, x be the favorable outcome as,

x = no. of times islanders win the game

Probability of success (p) =  $\frac{2}{7}$

Probability of failure (q) = $\frac{5}{7}$

So, the probability of x would be,

                      $x = n C_{r} \times(p)^{r} \times(q)^{n-r}$

                     $P(x=0) = 6 C_{0} \times\left(\frac{2}{7}\right)^{0} \times\left(\frac{5}{7}\right)^{6}$

                      $P(x=0) = 1 \times 1 \times \frac{(15625)}{117649} = 0.13281$