In a bag there are 8 red jelly beans and 7 green jelly beans. The 4 jelly beans are randomly chosen from the bag without replacement.

a)create a probability distribution table for choosing red jelly beans
b)what is the probability that at least 2 chosen jelly beans are green given that they are not all red?
Thanks.

a) To create a probability distribution table for choosing red jelly beans, we need to find the probability of selecting each number of red jelly beans from 0 to 4.

First, let's calculate the probability of selecting 0 red jelly beans:
The total number of jelly beans in the bag is 8 (red) + 7 (green) = 15.
Since all the beans chosen are not red, there must be only green beans. So, the probability of selecting 0 red beans is 7C4 / 15C4.
7C4 represents the number of ways to choose 4 green beans out of 7, and 15C4 represents the total number of ways to choose 4 beans out of 15.

Next, for the probability of selecting 1 red jelly bean:
We have 8 red jelly beans to choose from, and the remaining 3 beans must be green. Therefore the probability is 8C1 * 7C3 / 15C4.

For the probability of selecting 2 red jelly beans:
We have 8C2 ways to choose 2 red beans and 7C2 ways to choose 2 green beans, out of 15C4 possible combinations.

Similarly, for the probability of selecting 3 red jelly beans:
We have 8C3 ways to choose 3 red beans and 7C1 ways to choose 1 green bean, out of 15C4 possible combinations.

Finally, for the probability of selecting 4 red jelly beans:
We have 8C4 ways to choose 4 red beans, out of 15C4 possible combinations.

This calculation will give us a probability distribution table for choosing red jelly beans.

b) To find the probability that at least 2 chosen jelly beans are green, given that they are not all red, we need to consider two scenarios: 1) Exactly 2 green beans are chosen, and 2) 3 or 4 green beans are chosen.

For the first scenario, the probability can be calculated by adding the probability of choosing exactly 2 green beans and the probability of choosing exactly 3 green beans.

For the second scenario, the probability is the probability of choosing exactly 4 green beans.

To calculate these probabilities, we need to use the probability distribution table that we created earlier and sum up the relevant probabilities. Specifically, we need to sum up the probabilities of choosing exactly 2, 3, and 4 green beans, given that they are not all red.

Note: Given that the chosen jelly beans are not all red, the probability of choosing 0 green beans is not included in these calculations.

By summing up these probabilities, we can find the total probability that at least 2 chosen jelly beans are green, given that they are not all red.