Question

If P(A)=0.4, P(B)=0.5, and P(A ∩ B)=0.3, find thefollowing:

a) P(A U B)
b) P(A ∩ B')
c) P(A' U B')

Answer 1

The student's questions about probabilities were answered using fundamental probability formulas, resulting in P(A U B) = 0.6, P(A ∩ B') = 0.1, and P(A' U B') = 0.4.

Step-by-step explanation:

The student is asking about various probabilities involving two events, A and B. We have the following probabilities given: P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.3.

Find P(A U B)

To find the probability of A union B, P(A U B), we use the formula:

P(A U B) = P(A) + P(B) - P(A ∩ B)

Which in this case is 0.4 + 0.5 - 0.3 = 0.6. So, P(A U B) = 0.6.

Find P(A ∩ B')

Next, to find P(A ∩ B'), we need to subtract the probability of A and B from the probability of A, because A and not B (B') means A happens but B does not.

P(A ∩ B') = P(A) - P(A ∩ B)

Which gives us 0.4 - 0.3 = 0.1. So, P(A ∩ B') = 0.1.

Find P(A' U B')

Finally, to find P(A' U B'), we use De Morgan's laws which state:

P(A' U B') = 1 - P(A U B)

P(A' U B') is 1 - 0.6 = 0.4. So, the correct option for P(A' U B') is 0.4.