Question

The number of chips of different colors in Gail's bag is shown below:

3 blue chips
4 pink chips
8 white chips
Gail takes out a chip from the bag randomly without looking. She replaces the chip and then takes out another chip from the bag. What is the probability that Gail takes out a white chip in both draws?
A.
`(8)/(15)`+
`(7)/(14)`=
`(217)/(210)`
B.
`(8)/(15)`×
`(7)/(14)`=
`(56)/(210)`
C.
`(8)/(15)`+
`(8)/(15)`=
`(16)/(15)`
D.
`(8)/(15)`×
`(8)/(15)`=
`(64)/(225)`

Answer 1

most likely the probability is D because my mom said it is d i dont know how she got it

Answer 2

`(8)/(15) * (8)/(15)=(64)/(225)`

Explanation:

Given : 3 blue chips

4 pink chips

8 white chips

To Find: What is the probability that Gail takes out a white chip in both draws with replacement?

Solution:

Blue chips =3

Pink chips =4

White chips =8

Total chips = 3+4+8 =15

Now Probability of getting white chip on first draw =
`\frac{\text{Number of white chips }}{\text{Total no. of chips}}`

=
`(8)/(15)`

Now ,She replaces the chip and then takes out another chip from the bag.

So, Probability of getting white chip on second draw =
`(8)/(15)`

Probability of getting white chip in both draws =
`(8)/(15) * (8)/(15)=(64)/(225)`

Hence the probability that Gail takes out a white chip in both draws is
`(8)/(15) * (8)/(15)=(64)/(225)`

Thus Option D is correct.