Question

You have a box of chocolates (30 chocolates in the box). 15 are filled with caramel, 10 are filled with chocolate, and 5 are filled with cream. You and a friend pick a chocolate at random. What is the probability that you both pick chocolate

Answer 1

10.34% probability that you both pick chocolate

Explanation:

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

In this question, it is not important if you or your friends picks first. So we use the combinations formula to find the number of desired and total outcomes.

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:

10 are filled with chocolate, and we want to pick 2. So

`D = C_(10,2) = (10!)/(2!(10-2)!) = 45`

Total outcomes:

The box has 30 chocolates, and 2 are picked, so:

`T = C_(30,2) = (30!)/(2!(30-2)!) = 435`

Probability:

`P = (D)/(T) = (45)/(435) = 0.1034`

10.34% probability that you both pick chocolate