Question

1(a) Define the independence of two events A' and B. Given that A and B are independent events in a sample space, such that P(A) is 25 and P(AUB) = 0.8, find;

(i) P(B)
(ii) P(A'UB')
(b) In a certain town the probability that a person who owns a car is 0.25. Given that the probability that a person who owns a car is a university graduate is 0.2. Find the probability that a person selected at random owns a car and is a university graduate.​

Answer 1

The independence of two events A' and B means that the occurrence of one event does not affect the occurrence of the other. To find the probabilities in this scenario, use the formulas P(B) = P(A AND B) / P(A) and P(A'UB') = 1 - P(AUB). In the second part, the probability that a person selected at random owns a car and is a university graduate is found by multiplying the probabilities of owning a car and being a graduate together.

Step-by-step explanation:

The independence of two events A' and B means that the occurrence of event A' does not affect the occurrence of event B, and vice versa. To determine the probabilities in this scenario, we can use the formula for independent events: P(A AND B) = P(A) * P(B).

(i) To find P(B), we can rearrange the formula to P(B) = P(A AND B) / P(A) = 0.8 / 0.25 = 0.32.

(ii) To find P(A'UB'), we can use the formula P(A'UB') = 1 - P(AUB) = 1 - 0.8 = 0.2.

In part (b), since the probability of owning a car is 0.25 and the probability of being a university graduate is 0.2, we can multiply these probabilities together to find the probability that a person selected at random owns a car and is a university graduate: P(Car and Graduate) = 0.25 * 0.2 = 0.05.