Question

PLEASE HELP ME!!!

I have 5 pinks, 4 yellow, 3 orange, and 3 red starbursts. What is the probability that I will randomly pick a yellow starburst, put it back in the bag, and then randomly pick an orange starburst?

A. 7/15

B. 4/75

C. 4/15

D. 3/15

Answer 1

B. 4/75

Explanation:

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

For each trial:

The probabilities of picking each startbust are the same, so each event is independent.

Independent events:

Two events, A and B, we have that:

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

In this question:

Event A: Yellow starburst on the first trial.

Event B: Orange starbust on the second trial.

4 yellow out of 5+4+3+3 = 15 starbursts.

This means that
`P(A) = (4)/(15)`

3 orange out of 15 starbursts.

This means that
`P(B) = (3)/(15)`

Probability of A, then B:

`P(A \cap B) = P(A) * P(B) = (4)/(15) * (3)/(15) = (4*3)/(15*15) = (4)/(15*5) = (4)/(75)`

So the correct answer is:

B. 4/75