Question

If P(High) = 0.2, P(Low) = 0.8, P(Favorable | High) = 0.9, and P(Unfavorable | Low) = 0.7, calculate the following probabilities.

Answer 1

The student's question requires calculating probabilities using conditional probabilities and the law of total probability. For independent events, the joint probability is the product of their individual probabilities. Mutual exclusivity means the joint probability is zero.

Step-by-step explanation:

The student is asking to calculate certain probabilities using given conditional probabilities and the general probabilities of events. To solve for the requested probabilities, one can apply the rules of conditional probabilities and the law of total probability. For instance, we can use the formula P(A | B) = P(A AND B)/P(B) to find joint probabilities P(A AND B) when we know P(A | B) and P(B). Additionally, if events are independent, their joint probability is the product of their individual probabilities, as shown by P(A AND B) = P(A)P(B) when A and B are independent. Understanding these concepts allows us to solve a variety of probability questions.

For mutually exclusive events like H and D, P(HD) (the probability of both H and D occurring) is 0, since mutually exclusive events cannot happen at the same time. In the example where A and B are independent events, the joint probability P(A AND B) is the product of their individual probabilities, which would be 0.06 (0.2 * 0.3).