Question

Jerome is going to draw a marble from the bag shown below, replace it, and then draw another marble. What is the probability that Jerome will get a green or yellow marble on the first draw and a pink on the second draw?

Answer 1

The answer is 7/50.

To calculate this, a multiplication rule and an addition rule are used.

There are in total 20 marbles:

3 green + 4 yellow + 5 blue + 8 pink = 20 marbles.

The addition rule is used to calculate the probability of one of the events from multiple pathways. If you want that only one of the events happens, you will use the addition rule. We have two events from multiple pathways:

1. The probability that Jerome will get a green marble on the first draw is 3/20:

Of all 20 marbles, 3 of them are green. The probability that Jerome will get a green marble is 3/20.

2. The probability that Jerome will get a yellow marble on the first draw is 4/20:

Of all 20 marbles, 4 of them are yellow. The probability that Jerome will get a green marble is 4/20.

- Using the addition rule, the probability that Jerome will get a green or yellow marble on the first draw is 7/20:

3/20 + 4/20 = 7/20

The multiplication rule calculates the probability that both of two events will occur. In this method, the probabilities of each event are multiplied. Here we have two events:

1. The probability that Jerome will get a green or yellow marble on the first draw is 7/20.

2. The probability that Jerome will get a pink on the second draw is 8/20:

Of all 20 marbles, 8 of them are pink. The probability that Jerome will get a pink marble is 8/20.

- Using the multiplication rule, the probability that Jerome will get a green

or yellow marble on the first draw and a pink on the second draw is 7/50:
7/20 × 8/20 = 56/400 = 7/50