A jar contains four red, four yellow, and three green jelly beans. If Joan and Jim take one jelly bean each, the probability that they both take a red jelly bean is?
prob for Joan, then Jim = (4/11)(3/10) = 12/110 = 6/55
prob for Jim, then Joan = 6/55
so prob = 6/55 + 6/55 = 12/55
or
using combinations,
prob they both pick red
= C(4,1)xC(3,1)/C(11,2) = 12/55
To find the probability that Joan and Jim both take a red jelly bean, we need to calculate the probability of Joan taking a red jelly bean, and then multiply it by the conditional probability of Jim taking a red jelly bean given that Joan took one.
Let's calculate each probability step by step:
Step 1: Calculate the probability of Joan taking a red jelly bean.
To do this, we divide the number of red jelly beans by the total number of jelly beans.
Number of red jelly beans = 4
Total number of jelly beans = 4 (red) + 4 (yellow) + 3 (green) = 11
Probability of Joan taking a red jelly bean = Number of red jelly beans / Total number of jelly beans = 4 / 11 = 4/11
Step 2: Calculate the probability of Jim taking a red jelly bean given that Joan took one.
After Joan takes a red jelly bean, there are three red jelly beans left in the jar.
Total number of jelly beans remaining = 11 - 1 (Joan's pick) = 10
Number of red jelly beans remaining = 4 - 1 (Joan's pick) = 3
Probability of Jim taking a red jelly bean = Number of red jelly beans remaining / Total number of jelly beans remaining = 3 / 10 = 3/10
Step 3: Multiply the probabilities from steps 1 and 2 to find the probability that they both take a red jelly bean.
Probability that both Joan and Jim take a red jelly bean = Probability of Joan taking a red jelly bean * Probability of Jim taking a red jelly bean = (4/11) * (3/10) = 12/110 = 6/55
Therefore, the probability that Joan and Jim both take a red jelly bean is 6/55.