Question

Maria has eight black marbles, fourteen clear marbles, and twelve blue marbles in a bag. If she picks two marbles at random, without replacement, what is the probability that she will select a blue marble first, then a clear marble?

Answer 1

`\boxed{0.15}`

Explanation:

Part 1: Solve for the total amount of marbles

To solve for the probability of certain events, a population is needed to derive this information from. In order to find this population, add up the amounts of each marble.

8 + 14 + 12 = 34 marbles

Part 2: Determine the probabilities

Now, given the amounts of marbles, simply multiply the ratios of blue marbles to total marbles and the ratio of clear marbles to total marbles to get the combined probability.

`(12)/(34)*(14)/(33) = (28)/(187) \approxeq 0.1497 \approxeq 0.15 * 100 = 15`

The probability of these events occurring simultaneously is 15%.