Question

Two events A and B are independent and P(A)=41​ and P(B)=21​. Find: a. P(AB) b. P(A∪B) c. P(A∩B)

Answer 1

To find the probabilities of independent events A and B: P(AB) is the product of P(A) and P(B), P(A∪B) is calculated using the addition rule, and P(A∩B) is equivalent to P(AB).

Step-by-step explanation:

Calculating Probabilities of Independent Events

When calculating the probabilities of independent events, it's crucial to apply the basic principles of probability. For events A and B which are independent:

• The probability of both events A and B occurring, denoted as P(AB), is the product of their individual probabilities: P(A) × P(B).
• The probability of either event A or event B occurring, also known as the union of A and B and denoted as P(A∪B), is found using the addition rule: P(A) + P(B) - P(AB).
• Since the events are independent, the intersection P(A∩B) is equivalent to P(AB).

In this case, we have:

1. P(AB) = P(A) × P(B) = (1/4) × (1/2) = 1/8
2. P(A∪B) = P(A) + P(B) - P(AB) = (1/4) + (1/2) - (1/8) = 5/8
3. The intersection P(A∩B) is the same as P(AB), which is 1/8.

Therefore, the probabilities are:

• a. P(AB) = 1/8
• b. P(A∪B) = 5/8
• c. P(A∩B) = 1/8