a bag contains 4 red, 3 yellow, 3 blue, and 2 white marbles, for a total of 12 marbles. if lucia randomly…

Explanation:

Step1: Calculate probability of first - red marble

The probability of picking a red marble first is the number of red marbles divided by the total number of marbles. There are 4 red marbles and 12 total marbles, so $P(\text{first - red})=\frac{4}{12}$.

Step2: Calculate probability of second - white marble

After picking a red marble first (without replacement), there are now 11 marbles left. There are 2 white marbles. So $P(\text{second - white}|\text{first - red})=\frac{2}{11}$.

Step3: Calculate joint probability

By the multiplication rule for dependent events $P(A\cap B)=P(A)\times P(B|A)$. Here, $A$ is the event of picking a red marble first and $B$ is the event of picking a white marble second. So $P(\text{first - red and second - white})=\frac{4}{12}\times\frac{2}{11}=\frac{8}{132}=\frac{2}{33}$.

Answer:

$\frac{2}{33}$