Question

At the local ice cream shop, there

are 6 ice creams and 6 frozen
yogurts that look very similar, and
it's difficult to distinguish among
them. You scoop 1 scoop each
from 2 different barrels.
What is the possibility that both of
the scoops are ice cream?

Answer 1

22.73% possibility that both of the scoops are ice cream

Explanation:

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

The order of the scoops 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)!)`

What is the possibility that both of the scoops are ice cream?

Desired outcomes:

2 scoops of ice cream(set of 6). So

`D = C_(6,2) = (6!)/(2!4!) = 15`

Total outcomes:

2 scoops from a set of 6 + 6 = 12. So

`T = C_(12,2) = (12!)/(2!10!) = 66`

Probability:

`p = (D)/(T) = (15)/(66) = 0.2273`

22.73% possibility that both of the scoops are ice cream