Question

The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 50%. What is the probability that it will rain on exactly one of the three days they are there? Round your answer to the nearest thousandth.

Answer 1

The probability that it will rain on exactly one of the three days they are there is 0.375.

Given that Hiking Club plans to go camping in a State park where the probability of rain on any given day is 50%.

The binomial distribution is used when there are exactly two outcomes of a trial that are mutually exclusive.

Use binomial probability:

P = ⁿCʳ pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

probability of rain on any given day =p =0.50

total number of ways,n=3

let X is number of days with rain out of 3 days

So, $X\sim Bin(3,0.50)$

P(x=X)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ

P(x=1)=³C₁(0.50)¹(1-0.50)³⁻¹

P(x=1)=3×0.50×(0.5)²

P(x=1)=1.5×0.25

P(x=1)=0.375

Hence, the probability that it will rain on exactly one of the three days they are there where the probability of rain on any given day is 50% is 0.375.

Learn more about binomial ditribution from here brainly.com/question/15073378

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