Question

A bag contains 42 red marbles, 6 white marbles, and 8 gray marbles. You randomly pick out a marble, record its color, and put it back in the bag. You repeat this process 224 times. How many white or gray marbles do you expect to get?

Answer 1

`(14)/(56)` × 224=56 of the marbles to be either white or gray.

Explanation:

Answer 2

For any single draw,


`\mathbb P(\text{white})=\frac6{42+6+8}=\frac6{56}`

`\mathbb P(\text{gray})=\frac8{42+6+8}=\frac8{56}`

Drawing a white marble or a gray marble are disjoint events; only one of them can happen. So


`\mathbb P(\text{white or gray})=\mathbb P(\text{white})+\mathbb P(\text{gray})-\underbrace{\mathbb P(\text{white and gray})}_0`

`\mathbb P(\text{white or gray})=\frac6{56}+\frac8{56}=(14)/(56)`

Out of 224 draws, you should expect
`(14)/(56)*224=56` of the marbles to be either white or gray.