Question

If A and B are two events such that P(A) = 0.2, P(B) = 0.55 and P(A∩B)=0.1, then P(B∩A^c) is equal to

• A. 0.25
• B. 0.35
• C. 0.45
• D. 0.65
• E. 0.75

Answer 1

The Correct Option is C

Given: P(A) = 0.2, P(B) = 0.55, and P(A ∩ B) = 0.1. We are asked to find P(B ∩ A^c), which is the probability of event B occurring and event A not occurring.

Step 1: Use the formula for P(B): 

\[ P(B) = P(B \cap A) + P(B \cap A^c) \]

Step 2: Substitute the given values into the formula:

\[ 0.55 = 0.1 + P(B \cap A^c) \]

Step 3: Solve for P(B ∩ A^c):

\[ P(B \cap A^c) = 0.55 - 0.1 = 0.45 \]

Final Answer:

\[ 0.45 \]