Question

On a six-day vacation, the forecast is a 90 % chance of rain every day. What's the probability that it rains every day? Enter afraction or round your answer to 4 decimal places, if necessary.

Answer 1

0.5314 (53.14%)

Step-by-step explanation

Step 1: Given that:

The forecase of rain every day is 90% (0.9)

Step 2: To determine the probability that it will rain every day

Please note that the likelihood of rain on one day is unrelated to the likelihood of rain on another day

Now, we can compute the probability that it rains every day for the independent event by multiplying the individual probabilities.

This is the same as increasing the individual probability to the number of days because the individual probabilities are equal.

That is:

`\begin{gathered} \text{Prob = (0.9)}^6\text{ } \\ \text{ = 0.53144}1 \end{gathered}`

Hence, the probability that it rains every day is 0.5314 (rounded to 4 decimal places)