Final answer:
Jerry needs to pull out 3 socks to guarantee a matching pair. The probability calculations are based on the number of each color jelly bean divided by the total number of jelly beans.
Step-by-step explanation:
To ensure having a matching pair of socks, Jerry needs to pull out at most 3 socks. This is because, after pulling out two socks, there are two possibilities. Either he has pulled out two socks of the same color, in which case he already has a matching pair, or he has pulled out one black sock and one green sock. If he pulls out a third sock, it must either match the black sock or the green sock, guaranteeing a matching pair regardless of the color of the third sock.
Now, let's address the probability questions. The probabilities for selecting a jelly bean of each color can be computed as the number of jelly beans of that color divided by the total number of jelly beans in the jar.
- P(B) (probability of getting a blue jelly bean) = 26/150.
- P(G) (probability of getting a green jelly bean) = 20/150.
- P(P) (probability of getting a purple jelly bean) = 28/150.
- P(R) (probability of getting a red jelly bean) = 22/150.
- P(Y) (probability of getting a yellow jelly bean) = 38/150.
- P(O) (probability of getting an orange jelly bean) = (the rest of the jelly beans in the jar)/150.