A jar of jelly beans contains 50 red gumballs , 45 yellow gumballs, and 30 green gumballs. You reach into the jar and randomly select a jelly bean, then select another without putting the first jelly bean back. What is the probability that you draw two red jelly beans?
How can you draw jelly beans from a jar that contains gumballs?
To find the probability of drawing two red jelly beans, we need to calculate the probability of drawing a red jelly bean on the first draw and then drawing another red jelly bean on the second draw.
Step 1: Find the probability of drawing a red jelly bean on the first draw.
There are a total of 50 + 45 + 30 = 125 jelly beans in the jar.
The probability of drawing a red jelly bean on the first draw is calculated as the number of red jelly beans divided by the total number of jelly beans:
P(Red on first draw) = 50/125 = 2/5
Step 2: Find the probability of drawing another red jelly bean on the second draw.
After the first jelly bean is removed, there are now 124 jelly beans left in the jar, with 49 of them being red.
So, the probability of drawing a red jelly bean on the second draw is calculated as the number of remaining red jelly beans divided by the total number of remaining jelly beans:
P(Red on second draw) = 49/124 = 7/18
Step 3: Multiply the probabilities from the first and second draws together.
To find the probability of both events happening (drawing two red jelly beans), we multiply the individual probabilities:
P(Two red jelly beans) = P(Red on first draw) * P(Red on second draw)
P(Two red jelly beans) = (2/5) * (7/18)
P(Two red jelly beans) = 14/90
P(Two red jelly beans) = 7/45
Therefore, the probability of drawing two red jelly beans is 7/45.