Question

the cooler contains 10 grape juice bottles and 15 cranberry juice bottles. you randomly choose 2 bottles. what probability that both bottles are cranberry juice?

Answer 1

35% probability that both bottles are cranberry juice

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The orders in which the bottles are chosen is not important, so we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

Desired outcomes:

2 bottles of cranberry juice from a set of 15. So

`D = C_(15,2) = (15!)/(2!13!) = 105`

Total outcomes:

2 bottles from a set of 15+10 = 25 bottles. So

`T = C_(25,2) = (25!)/(2!23!) = 300`

Probability:

`P = (D)/(T) = (105)/(300) = 0.35`

35% probability that both bottles are cranberry juice