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.
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.