Question

given p(a) = 0.4 and p(b) = 0.3, do the following. (a) if a and b are mutually exclusive events, compute p(a or b). (b) if p(a and b) = 0.2, compute p(a or b).

Answer 1

For mutually exclusive events, P(A OR B) is the sum of the probabilities of each event, resulting in 0.7. If P(A AND B) is 0.2, indicating they are not mutually exclusive, then P(A OR B) is calculated using the general addition rule, resulting in 0.5.

Step-by-step explanation:

Given P(A) = 0.4 and P(B) = 0.3, let's solve for P(A OR B) under different conditions:

(a) If A and B are Mutually Exclusive

For mutually exclusive events, the probability of either A or B occurring is simply the sum of their individual probabilities because they cannot occur at the same time. Therefore, P(A OR B) = P(A) + P(B), which gives P(A OR B) = 0.4 + 0.3 = 0.7.

(b) If P(A AND B) = 0.2

When given P(A AND B) = 0.2, these events are not mutually exclusive. We must then use the general addition rule for any two events: P(A OR B) = P(A) + P(B) − P(A AND B). Substituting the given probabilities, we have P(A OR B) = 0.4 + 0.3 − 0.2 = 0.5.