Question

Suppose you choose a marble from a bag containing 3 red marbles, 5 white marbles, and 4 blue

marbles. You return the first marble to the bag and then choose again. Find P (red and blue).

Answer 1

P(red and blue) = 1/12

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Probability of independent events:

If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each event happening, that is:

`P(A \cap B) = P(A)P(B)`

P (red and blue).

Probability of choosing a red marble, then a blue marble. The marbles are replaced, so the trials are independent.

Probability of a red marble:

3 out of 3 + 5 + 4 = 12. So

`P(A) = (3)/(12) = (1)/(4)`

Probability of a blue marble:

4 out of 12, so:

`P(B) = (4)/(12) = (1)/(3)`

P (red and blue).

`P(A \cap B) = P(A)P(B) = (1)/(4) * (1)/(3) = (1)/(4*3) = (1)/(12)`

So

P(red and blue) = 1/12