Question

Three independent events, A, B and C occur with probabilities P(A) = 1/2, P(B) = 1/3, P(C) = 1/4. What is the probability that at least one of the three events occurs
1. 2/3
2. 1/4
3. 3/4
4. 1/12

Answer 1

Correct Answer - Option 3 : 3/4

Concept:

Probability of event happening = 1 - Probability of event not happening 

 

Calculation:

Here, P(A) = 1/2, P(B) = 1/3, P(C) = 1/4. 

Probability of at least one of the three events occurs = 1 - None of the event occuring

= 1 - (1 - 1/2) × (1 - 1/3) × (1 - 1/4)

= 1 - (1/2) × (2/3) × (3/4)

= 1 - 1/4

= 3/4

Hence, option (3) is correct.