Question

Given the following information, answer questions a - d.

P(A) = 0.44
P(B) = 0.49
A and B are independent.
Round all answers to 5 decimal places as needed
a) Find P( A∩ B).
b) Find P( A∪B).
c) Find P( A ∣ B).
d) Find P( B∣A).

Answer 1

To find the probabilities in this problem, use formulas for calculating the intersection, union, and conditional probabilities. The probability of the intersection is 0.2156, the probability of the union is 0.7144, the conditional probability of A given B is 0.4408, and the conditional probability of B given A is 0.4909.

Step-by-step explanation:

To solve the problem, we need to use the formula for the probability of the intersection of two independent events, which is P(A ∩ B) = P(A) * P(B). Since P(A) = 0.44 and P(B) = 0.49, we can substitute these values into the formula. P(A ∩ B) = 0.44 * 0.49 = 0.2156. Therefore, P(A ∩ B) is 0.2156.

To find the probability of the union of two events, we can use the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Using the previously calculated values, P(A ∪ B) = 0.44 + 0.49 - 0.2156 = 0.7144. Therefore, P(A ∪ B) is 0.7144.

The conditional probability, P(A | B), is calculated using the formula P(A | B) = P(A ∩ B) / P(B). Substituting the values, we get P(A | B) = 0.2156 / 0.49 = 0.4408. Therefore, P(A | B) is 0.4408.

The conditional probability, P(B | A), is calculated using the formula P(B | A) = P(A ∩ B) / P(A). Substituting the values, we get P(B | A) = 0.2156 / 0.44 = 0.4909. Therefore, P(B | A) is 0.4909.