Ramesh passed the government exam 8 out of 10 times, and Bala passed the government exam 6 out of 8 times. Find the probability that at least one will fail the government exam?

1. 6/20

2. 7/24

3. 7/20

4. 7/10

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Correct Answer – Option 3 : 7/20

Given:Probability of Ramesh passing the government exam, P(A) = 8/10

Probability of Bala passing the government exam, P(B) = 6/8

Concept used :Probability = number of favourable outcomes /total number of outcome

⇒ P(A) × P(B’) + P(A’) × P(B)

Calculation:The probability that Ramesh and Bala fails is

⇒ P(A’) fails = 2/10

⇒ P(B’) fails = 2/8

Probability that any one fail = P(A) × P(B’) + P(A’) × P(B)

⇒ (8/10) × (2/8) + (2/10) × (6/8) = 1/5 + 3/20

⇒ 7/20

∴ The probability that Ramesh and Bala fails is 7/20