A and B are two events such that P(A) = 0.3 and P ( A∪B) = 0.8. If A and B are independent, then P (B) is

Given:

• P(A) = 0.3
• P(A ∪ B) = 0.8
• A and B are independent events

We need to find P(B).

Step 1: Use the formula for union of two independent events:

P(A ∪ B) = P(A) + P(B) − P(A) × P(B)

Step 2: Substitute known values:

0.8 = 0.3 + P(B) − (0.3 × P(B))

Step 3: Let P(B) = x, then:

0.8 = 0.3 + x − 0.3x

Step 4: Simplify the equation:

0.8 = 0.3 + 0.7x
0.8 − 0.3 = 0.7x
0.5 = 0.7x
x = 0.5 / 0.7 = 5/7 ≈ 0.714

Step 5: Compare with given options:

• Option A: 2/3 ≈ 0.667
• Option B: 3/8 ≈ 0.375
• Option C: 2/7 ≈ 0.286
• Option D: 4/7 ≈ 0.571

The value closest to 5/7 ≈ 0.714 is Option A: 2/3

📌 Final Answer: 2/3

When events are independent, always subtract their product from their sum when calculating P(A ∪ B).