Question

The number of marbles of different colors stored in a hat is listed below:

8 red marbles
10 green marbles
6 blue marbles
Without looking in the hat, Tessa takes out a marble at random. She replaces the marble and then takes out another marble from the hat. What is the probability that Tessa takes out a blue marble in both draws?

fraction 1 over 16

fraction 1 over 12

fraction 1 over 4

fraction 1 over 2


It's not 1/4 because I tried that.

Answer 1

There is a 1/4 chance of getting the Blue Marble out of the bag. But when it is 2 in a row you have to multiply your chances so it would be 1/4 * 1/4 or 1/16

Answer 2

`(1)/(16)`

Explanation:

Given : The number of marbles of different colors stored in a hat is listed below:

8 red marbles

10 green marbles

6 blue marbles

To Find: What is the probability that Tessa takes out a blue marble in both draws?

Solution:

8 red marbles

10 green marbles

6 blue marbles

Total Marbles = 8+10+6= 24

Probability of getting blue marble on first draw =
`\frac{\text{No. of blue marbles}}{\text{Total no. of marbles}}`

Probability of getting blue marble on first draw =
`(6)/(24)`

Now the marble is replaced

Probability of getting blue marble on second draw =
`\frac{\text{No. of blue marbles}}{\text{Total no. of marbles}}`

Probability of getting blue marble on second draw =
`(6)/(24)`

So, probability of getting blue marble on both the draws =
`(6)/(24) * (6)/(24)`

=
`(36)/(576)`

=
`(1)/(16)`

Hence the probability that Tessa takes out a blue marble in both draws is
`(1)/(16)`