Question

Studies have shown that 541/1000  of people in Florida do not stay out in the sun for more than one hour per day.  If 3 Floridians are selected at random, find the probability that all three will not stay out in the sun for more than one hour.  HINT: THIS IS LIKE A BOTH PROBLEM EXCEPT THERE ARE MULTIPLE EVENTS

give the answer in a unreduced fraction, 4 place decimal and 2 place in %.

Answer 1

The probability that a randomly selected people in Florida do not stay out in the sun for more than one hour per day

Let X denotes the number of people in Florida do not stay out in the sun for more than one hour per day among 3 randomly selected Floridians.

Here,

X ~ Binomial(n = 3, p = 0.541)

The probability mass function of X is

Now,

The probability that all three will not stay out in the sun for more than one hour

= 15.83%