Final answer:
There is a discrepancy in the probability values given for the events E and F. The probability of P(E ∩ F) cannot be greater than P(E). Review the values to correct the mistake.
Step-by-step explanation:
The question is asking about the probability of the intersection of two events, specifically P(E ∩ F). However, there seems to be a typo in the question because the probability of the intersection of two events cannot be greater than the probability of either event individually. In the question, P(E) is given as 0.3 and P(E ∩ F) is stated as 0.4, which is not possible since P(E ∩ F) can't exceed P(E).
To find P(E∩F), we need to use the formula P(E∩F) = P(E) × P(F|E), where P(E) is the probability of event E occurring, P(F|E) is the probability of event F occurring given that event E has occurred, and P(E∩F) is the probability of both events E and F occurring.
Given that P(E) = 0.3 and P(F∩E) = 0.4, we can substitute these values into the formula.
P(F∩E) = P(E) × P(F|E)
0.4 = 0.3 × P(F|E)
To solve for P(F|E), divide both sides of the equation by 0.3:
P(F|E) = 0.4 / 0.3 = 1.33
Therefore, the probability of P(E∩F) is 1.33.