Question

Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find P(red and blue).

Answer 1

`(7)/(9)`

Explanation:

Given : A bag containing 4 red marbles, 2 white marbles, and 3 blue marbles.

You return the first marble to the bag and then choose again.

To Find: Find P(red and blue).

Solution:

A bag containing 4 red marbles, 2 white marbles, and 3 blue marbles.

Total marbles = 4+2+3=9

Probability of getting red marble on first draw =
`\frac{\text{No. of red marbles}}{\text{No. of total marbles}}`

=
`(4)/(9)`

Now we are given that You return the first marble to the bag and then choose again.

So,Total no. of marbles will remain same.

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

=
`(3)/(9)`

Now P(red and blue) =
`(4)/(9)+(3)/(9)`

=
`(7)/(9)`

Hence P(red and blue) is
`(7)/(9)`.

Answer 2

4 + 2 + 3 = 9 total marbles

4 are red so you have a 4/9 chance of picking a red

there are 3 blue so you have a 3/9 ( reduces to 1/3) chance of picking a blue one

4/9 * 1/3 = 4/27 probability of picking a read and a blue marble