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? (3 green, 4 yellow, 5 blue, 8 pink)

7/50
3/8
27/200

Answer 1

7/50

Explanation:

Answer 2

The answer is 7/50.

To solve this, we divide it into two: the first and the second draw.
So, for the first draw;
P(Green) = 3/20 [we got 20 marbles in total]
P(Yellow) = 4/20
Since we are asked for the probability of getting a green OR a yellow marble on the first draw (mind the wording), we will be adding these two probabilities:
P(Green) + P(Yellow) ⇒ 3/20 + 4/20 = 7/20
This means that Jerome has a 7/20 chance of drawing either a green or a yellow marble on his first draw.

Now, unto the second draw!
Since we have a replacement for the first drawn marble, we would still have a total of 20 marbles in the bag. So, we multiply 7/20 by whatever probability we have from drawing a pink marble on the second draw.
We have 8 pink marbles. Therefore, P(Pink) = 8/20. We then multiply this by 7/20:

P(Green/Yellow and Pink) = 7/20 x 8/20 = 56/400
Simplify: 56/400 ⇒ 7/50

Thus, the probability that Jerome will get a green or a yellow marble on the first draw and a pink one on the second draw would be 7/50.
Tip for life: When working with probabilities, "or " means addition while "and" means multiplication. (Example: probability of red or blue ⇒ P(red) + P(blue), etc.)


Hope this helps.