Question

A bag contains 5 green marbles, 8 red marbles, 11 orange marbles, 7 brown marbles, and 12 blue marbles. You choose a marble, replace it, and choose again. What is P(red, then blue)?

Answer 1

96/1849

Explanation:

You have 43 marbles in total.

Probability of picking red first:

P(red) =

Probability of picking blue:

P(blue) =

Note that the denominator is still 43 because the marble is replaced.

An important part of the question is that you're picking red, then blue. So you only care about the situations where red is picked first.

Total probability is:

P(red, then blue) = * = ≈ 0.052

Answer 2

You have 43 marbles in total.

Probability of picking red first:
P(red) =
`(8)/(43)`

Probability of picking blue:
P(blue) =
`(12)/(43)`
Note that the denominator is still 43 because the marble is replaced.

An important part of the question is that you're picking red, then blue. So you only care about the situations where red is picked first.

Total probability is:
P(red, then blue) =
`(8)/(43)` *
`(12)/(43)` =
`(96)/(1849)` ≈ 0.052