Final answer:
In this question, we are given mutually exclusive events q and r with probabilities p(q) = 0.45 and p(r) = 0.30. We can find the probabilities of their intersection, conditional probability of q given r, and the probability of either q or r happening using probability formulas.
Step-by-step explanation:
In this question, we are given that events q and r are mutually exclusive, which means they cannot happen at the same time. We are also given the probabilities of p(q) = 0.45 and p(r) = 0.30.
a. To find the probability of both events happening, we need to find the intersection of the two events, denoted as p(q ∩ r). Since q and r are mutually exclusive, the probability of their intersection is 0. So, p(q ∩ r) = 0.
b. To find the conditional probability of event q given that event r has occurred, denoted as p(q|r), we use the formula p(q|r) = p(q ∩ r) / p(r). Since p(q ∩ r) = 0, p(q|r) = 0.
c. To find the probability of either event q or event r happening, denoted as p(q or r), we use the formula p(q or r) = p(q) + p(r) - p(q ∩ r). Substituting the given probabilities, we have p(q or r) = 0.45 + 0.30 - 0 = 0.75.