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?
Drawing a white marble or a gray marble are disjoint events; only one of them can happen. So
[tex]\mathbb P(\text{white or gray})=\mathbb P(\text{white})+\mathbb P(\text{gray})-\underbrace{\mathbb P(\text{white and gray})}_0[/tex] [tex]\mathbb P(\text{white or gray})=\dfrac6{56}+\dfrac8{56}=\dfrac{14}{56}[/tex]
Out of 224 draws, you should expect [tex]\dfrac{14}{56}\times224=56[/tex] of the marbles to be either white or gray.
