Question

on a five day vacation the forecast is an 85 percent chance of rain every day what's the probability that it rains every day

Answer 1

0.4437

Explanation:

Forecast that it rains every day = 85% = 0.85

The probability that it will rain is independednt on the number of days it rains.

The probability that it rains each day will be the same irrespective of the number of days

For 5 days of vacation, the probability it will rain every day:

$\begin{gathered} Pr\text{ (rain every day for 5 days) = 0.85 }\times\text{ 0.85 }\times0.85\text{ }\times\text{ 0.85 }\times0.85 \\ Pr(rain\text{ }everyday\text{ }for\text{ }5days)=\mleft(0.85\mright)^5 \end{gathered}$$Pr(rain\text{ }everyday\text{ }for\text{ }5days)=\text{ 0.4437 ( 4 decimal place)}$