Question

A local grocery store receives strawberries from suppliers in Florida and California. Currently there are 18 strawberry containers on the shelf and 11 of them are from Florida. A shopper selects three containers to purchase. What is the probability that exactly one of the containers is from the Florida supplier

Answer 1

You have 11/18 probability when choosing one container and when choosing three containers out of 2 choices we will first denote F and C respectively for the choice of states, and the possible outcomes are FFF, FFC, FCC, and CCC so possibility for at least one from Florida is 3/4. 11/18*3/4 will be your answer.

Answer 2

Using the hypergeometric distribution, it is found that there is a 0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.

The containers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

• x is the number of successes.
• N is the size of the population.
• n is the size of the sample.
• k is the total number of desired outcomes.

In this problem:

• There are 18 containers, hence $N = 18$
• 11 of those are in Florida, hence $k = 11$.
• A sample of 3 containers is taken, hence $n = 3$

The probability that exactly one of the containers is from the Florida supplier is P(X = 1), hence:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 1) = h(1,18,3,11) = \frac{C_{11,1}C_{7,2}}{C_{18,3}} = 0.2831$

0.2831 = 28.31% probability that exactly one of the containers is from the Florida supplier.

A similar problem is given at https://brainly.com/question/24826394