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
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
1. 6/20
2. 7/24
3. 7/20
4. 7/10
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