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

$\frac{14}{56}$ × 224=56 of the marbles to be either white or gray.

Step-by-step explanation:

Answer 2

For any single draw,

$\mathbb P(\text{white})=\dfrac6{42+6+8}=\dfrac6{56}$
$\mathbb P(\text{gray})=\dfrac8{42+6+8}=\dfrac8{56}$

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

$\mathbb P(\text{white or gray})=\mathbb P(\text{white})+\mathbb P(\text{gray})-\underbrace{\mathbb P(\text{white and gray})}_0$
$\mathbb P(\text{white or gray})=\dfrac6{56}+\dfrac8{56}=\dfrac{14}{56}$

Out of 224 draws, you should expect $\dfrac{14}{56}\times224=56$ of the marbles to be either white or gray.