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?
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.
\(\frac{14}{56}\) × 224=56 of the marbles to be either white or gray.
Step-by-step explanation: