Question

www.g "Suppose a jar contains 18 red marbles and 16 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Round your answer to 4 decimal places."

Answer 1

0.2727 = 27.27% probability that both are red.

Explanation:

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

In this question, the order in which the marbles are selected is not important. So we use the combinations formula to solve.

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 red marbles, from a set of 18. So

`D = C_(18,2) = (18!)/(2!16!) = 153`

Total outcomes:

Two marbles from a set of 18 + 16 = 34. So

`T = C_(34,2) = (34!)/(2!32!) = 561`

Probability:

`p = (D)/(T) = (153)/(561) = 0.2727`

0.2727 = 27.27% probability that both are red.