Question

1)Find the probability that: both are blue2) Find the probability that: they are the same color3) Find the probability that:At least one is red4) Find the probability that: exactly one is yellow

Answer 1

The bag contains 3 red marbles, 4 yellow and 5 blue.

In total we have 12 marbles.

The probability of selecting one blue one will be 5 out of 12.

We will select for a second time, after replacing the first marble. This second case, the probability will be again of 5 out of 12.

Both events are independent because we are replacing the first selected marble. The probability of two independent events to occur is the product of the individual probability of each event. Then, the probability of selecting a blue marble in the 2 events is:

$\frac{5}{12}\cdot\frac{5}{12}=\frac{25}{144}\approx0.1736$