A botanical research group is studying seed variations across two germination trays, Alpha and Beta. Tray Alpha contains 7 seeds: 4 are Crimson (CCC) and 3 are Gold (GGG). Tray Beta contains 5 seeds: 2 are Crimson and 3 are Gold.
Two seeds are selected sequentially without replacement from Tray Alpha and transplanted into Tray Beta. Subsequently, a single seed is drawn from the resulting 7 seeds in Tray Beta.
Calculate the probability that both seeds transplanted from Tray Alpha are the same color. Let this be event AAA.
Find P(B)P(B)P(B), where B B\,B is the event that the final seed drawn from Tray Beta is Crimson.
Find P(A∩B)P(A \cap B)P(A∩B).
Determine the value of P(A∪B)P(A \cup B)P(A∪B).
Given that all three seeds selected during the process (the two from Alpha and the one from Beta) are the same color, find the probability that they are all Crimson.
