If A and B are mutually exclusive events such that P(A) P(B) > 0, then which option is correct?

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )

Answer 1

The correct answer is: "A and B are not independent."

Key Points

mutually exclusive events:
- Mutually exclusive events are also known as disjoint or incompatible events.
- Mutually exclusive events are events that cannot occur simultaneously.
- In other words, if one event occurs, the other event cannot occur.
If two events A and B are mutually exclusive, then the probability of their union is equal to the sum of their individual probabilities:
- \(P(A ∪ B) = P(A) + P(B).\)
If two events are mutually exclusive, they are not independent. Independence means that the occurrence of one event does not affect the probability of the other event.
A proper subset is a subset in which the set is not equal to the original set. So, A ⊂ B is not a correct answer in this case.

Additional Information

Mutually exclusive events are also known as disjoint or incompatible events
Independence means that the occurrence of one event does not affect the probability of the other event
Understanding the concept of mutually exclusive events is important in probability theory as it helps to calculate the probability of the union of two or more events.
Understanding the relationship between mutually exclusive events and independence is also important as it helps to determine the relationship between different events in a probability model.