Question

A and B are two independent events. If the probability of event A is P(A) = 0.7, and the probability of event B is P(B) = a, and the probability of the union of events A and B is P(A ∪ B) = 0.8, then what is the value of 'a'?

Answer 1

The value of 'a' is 0.1.

Step-by-step explanation:

To find the value of 'a', we can use the formula for the probability of the union of two independent events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Since A and B are independent, P(A ∩ B) = 0. Therefore, we have 0.8 = 0.7 + a - 0. Multiplying through by 10, we get 8 = 7 + 10a - 0. Simplifying, we find that 1 = 10a. Dividing both sides by 10, we get a = 0.1.