Question

If P(E∩F)=0.18,P(E∣F)=0.24, And P(F∣E)=0.8, Then

(A) P(E)= ?
(B) P(F)= ?
(C) P(E∪F)= ?

Answer 1

Using the definitions of conditional probability and the relationship between joint probability and marginal probabilities, we found P(E) = 0.225, P(F) = 0.75, and P(E∪F) = 0.795.

Step-by-step explanation:

To solve this problem, we will use the definitions of conditional probability and the relationship between joint probability and marginal probabilities.

We have the following probabilities given:

P(E∩F) = 0.18 (The probability that both events E and F occur)

P(E|F) = 0.24 (The conditional probability that event E occurs given that F has occurred)

P(F|E) = 0.8 (The conditional probability that event F occurs given that E has occurred)

From the definition of conditional probability, we know:

P(E|F) = P(E∩F) / P(F) and P(F|E) = P(E∩F) / P(E)

Using these equations, we can calculate P(E) and P(F):

P(E) = P(E∩F) / P(F|E) = 0.18 / 0.8 = 0.225

P(F) = P(E∩F) / P(E|F) = 0.18 / 0.24 = 0.75

To calculate P(E∪F), we use the formula:

P(E∪F) = P(E) + P(F) - P(E∩F)

P(E∪F) = 0.225 + 0.75 - 0.18 = 0.795

Therefore, the answers are:

P(E) = 0.225

P(F) = 0.75

P(E∪F) = 0.795