Final answer:
A. P(E ∩ F) = 0.51, B. P(E ∩ Fᶜ) = 0, C. P(E ∪ F) = 0.51
Step-by-step explanation:
A. P(E ∩ F):
To find the probability of the intersection of two events, we can use the formula: P(E ∩ F) = P(E) + P(F) - P(E ∩ Fᶜ).
From the given information, we have P(E) = 0.35 and P(F) = 0.67. To find P(E ∩ F), we need to know P(E ∩ Fᶜ).
To find P(E ∩ Fᶜ), we can use the formula: P(E ∩ Fᶜ) = P(E) - P(E ∩ F).
From the given information, we have P(E ∩ Fᶜ) = 0.86 - P(E) = 0.86 - 0.35 = 0.51.
Now, we can calculate P(E ∩ F) = P(E) + P(F) - P(E ∩ Fᶜ) = 0.35 + 0.67 - 0.51 = 0.51.
Therefore, the probability of the intersection of events E and F is 0.51.
B. P(E ∩ Fᶜ):
To find the probability of the intersection of event E and the complement of event F, we can use the formula: P(E ∩ Fᶜ) = P(E) - P(E ∩ F).
From the given information, we have P(E) = 0.35 and P(E ∩ F) = 0.51.
Therefore, the probability of the intersection of event E and the complement of event F is 0.35 - 0.51 = -0.16.
However, probabilities cannot be negative, so the correct answer would be 0.
C. P(E ∪ F):
To find the probability of the union of two events, we can use the formula: P(E ∪ F) = P(E) + P(F) - P(E ∩ F).
From the given information, we have P(E) = 0.35, P(F) = 0.67, and P(E ∩ F) = 0.51.
Therefore, the probability of the union of events E and F is 0.35 + 0.67 - 0.51 = 0.51.