Question

If P(A)=2/3, P(B)=4/5, and P(A U B) =11/15, what is P(A ∩ B)?

Answer 1

Answer:

P(A ∩ B) = $\frac{11}{15}$

Step-by-step explanation:

If P(A)=2/3, P(B)=4/5, and P(A U B) =11/15

we need to find out  P(A ∩ B)

P(A U B) = P(A) + P(B) - P(A ∩ B)

Now we add P(A ∩ B) on both sides and subtract P(A U B) from both sides

P(A ∩ B) = P(A) + P(B)- P(A U B)

now we plug in the values

P(A ∩ B) = $\frac{2}{3} + \frac{4}{5} - \frac{11}{15}$

Make the denominators same . LCD  is 15

P(A ∩ B) = $\frac{10}{15} + \frac{12}{15} - \frac{11}{15}$

P(A ∩ B) = $\frac{22}{15}-\frac{11}{15}$

P(A ∩ B) = $\frac{11}{15}$

Answer 2

The answer is A on apex