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 [tex]\frac{2}{7}[/tex].
So, probability that the islanders will not beat the rangers in the game is = [tex]1-\frac{2}{7}=\frac{5}{7}[/tex]
Let, x be the favorable outcome as,
x = no. of times islanders win the game
Probability of success (p) = [tex]\frac{2}{7}[/tex]
Probability of failure (q) = [tex]\frac{5}{7}[/tex]
So, the probability of x would be,
[tex]x = n C_{r} \times(p)^{r} \times(q)^{n-r}[/tex]
[tex]P(x=0) = 6 C_{0} \times\left(\frac{2}{7}\right)^{0} \times\left(\frac{5}{7}\right)^{6}[/tex]
[tex]P(x=0) = 1 \times 1 \times \frac{(15625)}{117649} = 0.13281[/tex]
