Suppose you are scooping ice cream for 20 little kids Given

Suppose you are scooping ice cream for 20 little kids. Given that you are a master of telepathy, you are able to determine their favorite avor with 80% certainty.

a. Declare a random variable for the number of kids that received their favorite avor of ice cream and provide the expected value and variance.

b. Find the probability that at least 2 kids receive their favorite avor.

Solution

Suppose you are scooping ice cream for 20 little kids. Given that you are a master of telepathy, you are able to determine their favorite avor with 80% certainty.

a. Declare a random variable for the number of kids that received their favorite avor of ice cream and provide the expected value and variance.

A binomial random variable is the number of successes x in n repeated trials of a binomial experiment.

Here the trials is 20 and fixed probability is 0.80.

Here the binomial random variable is the number of kids that received their favorite avor of ice cream

n=20

P=0.8

Expectation = np = 16

Variance = np(1 - p) = 3.2

Standard deviation = 1.78885

b. Find the probability that at least 2 kids receive their favorite avor.

P( x >=2 ) = 1- ( P( x=0)+P( x=1) )    = 1 - (0+0) =1

The required probability = 1