The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 83% . What is the probability that it will rain on exactly zero of the five days they are there?Round your answer to the nearest thousandth.

Question

Answer 1

To solve this problem, we can use the binomial probability formula. The binomial probability formula is given by:

where:-

is the number of trials (in this case, 5 days),-

is the number of successes (in this case, 0 days of rain),-

is the probability of success on a single trial (in this case, 0.83 for rain),-

is the binomial coefficient, calculated as \( \frac{n!}{k!(n-k)!} \).Given:-

-

First, calculate the binomial coefficient

:

Next, calculate

and \( (1-p)^{n-k} \):

Now, compute

:

Finally, multiply these values together to get the probability:

Rounding to the nearest thousandth, the probability that it will rain on exactly zero of the five days they are there is approximately

.

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