Consider the following.

P(A) = 0.27 and P(B) = 0.36,
A and B are mutually exclusive events

(a) Find the probability P(A). (Give your answer correct to two decimal places.)


(b) Find the probability P(B). (Give your answer correct to two decimal places.)


(c) Find the probability P(A or B). (Give your answer correct to two decimal places.)


(d) Find the probability P(A and B). (Give your answer correct to two decimal places.)

To find the probabilities for the given events, we can use the formulas associated with these types of probabilities. Let's go through each question one by one:

(a) To find the probability of event A, we are given that P(A) is equal to 0.27. Therefore, the probability of event A is P(A) = 0.27.

(b) To find the probability of event B, we are given that P(B) is equal to 0.36. Therefore, the probability of event B is P(B) = 0.36.

(c) To find the probability of event A or B, we need to find the sum of their individual probabilities since they are mutually exclusive events. The formula for the union of mutually exclusive events is P(A or B) = P(A) + P(B). Plugging in the given values, we get P(A or B) = 0.27 + 0.36 = 0.63.

(d) Since A and B are mutually exclusive events, the probability of both A and B occurring at the same time (P(A and B)) is zero. This is because if they are mutually exclusive, they cannot happen simultaneously. Therefore, P(A and B) = 0.

So, to summarize:

(a) P(A) = 0.27
(b) P(B) = 0.36
(c) P(A or B) = 0.63
(d) P(A and B) = 0