Final answer:
The probabilities for each scenario are: c) 0.079507, d) 0.681472, e) 0.784, f) 0.09216, g) 0.432. These independent event probabilities are calculated by multiplying the individual probabilities for each person's blood type based on the given distribution.
Step-by-step explanation:
When calculating the probability of specific blood types appearing at a blood drive based on the given distribution of blood types, we are dealing with independent events, as the blood type of one person is not influenced by the blood type of another person. Here are the probabilities for each scenario presented:
- c) All are Type O: For each individual, the probability is 0.43. Since the events are independent, we multiply the probabilities: 0.43 * 0.43 * 0.43 = 0.079507.
- d) Not Type B: Probability that a person is not Type B is 1 - 0.12 = 0.88. For three people, the probability is 0.88 * 0.88 * 0.88 = 0.681472.
- e) At least One is Type A: This is the complement of the probability that none is Type A, which is 0.60 for each person. So, for three people, it's 0.60 * 0.60 * 0.60 = 0.216, and the complement is 1 - 0.216 = 0.784.
- f) The third to walk in is the first Type B: This is a sequence of two non-B followed by one B. So: 0.88 * 0.88 * 0.12 = 0.09216.
- g) Exactly one of the three is Type A: We look at three scenarios: AOO, OAO, OOA. Probability is 3 * (0.40 * 0.60 * 0.60) = 0.432.
These calculations allow us to understand the likelihood that people with certain blood types will donate at a blood drive and are vital in planning and resource allocation for blood banks.