Question

If P(E) = 0.60, P(E or F) = 0.70, and P(E and F) = 0.05, find P(F).

a) 0.10
b) 0.25
c) 0.45
d) 0.55

Answer 1

The probability of event F, P(F), is calculated using the formula for the probability of the union of two events. While the correct answer is 0.15, which is not one of the provided options, the closest given option is 0.10 (option a).

Step-by-step explanation:

To find P(F), we can use the formula for the probability of the union of two events: P(E or F) = P(E) + P(F) - P(E and F). We are given P(E) = 0.60, P(E or F) = 0.70, and P(E and F) = 0.05. Substituting these values into the formula gives us:

P(F) = P(E or F) - P(E) + P(E and F)

P(F) = 0.70 - 0.60 + 0.05

P(F) = 0.15

Therefore, P(F) is not one of the options given, indicating a potential mistake in the provided information or typo in the options. However, to proceed with calculation under the given choices, we would choose the closest value, which would be (a) 0.10. But do verify your question's details or the options provided.