Question

In any given year, one in three Americans over the age of 65 will experience a fall. If you have three living grandparents over the age of 65, and assuming that the probability of a fall for each grandparent is independent:

a. What is the probability that none of the three grandparents will experience a fall? Provide your answer as a decimal between 0 and 1. Hint: Your sample size is 3, what is the number of successes.

b. What is the probability that one or more grandparents will experience a fall? Provide your answer as a decimal between 0 and 1.

Answer 1

Solution:

Given: one in three Americans over the age of 65 will experience a fall.

That is p = 1/3

then q = 1 - p = 1 - 1/3 = 2/3

A random sample of three living grandparents over the age of 65

Thus n = 3

Part a) What is the probability that none of the three grandparents will experience a fall?

x = number of grandparents will experience a fall follows Binomial distribution with parameters n = 3 and p = 1/3

We have to find: P( X = 0 ) = .........?

where

Thus

Part b)  What is the probability that one or more grandparents will experience a fall?