If A and B are two mutually exclusive events and P(A) = 2/3 and P(B) = 4/9, then find the probability of the occurrance of A and B together.Correct answer is '0'. Can you explain this answer?

Question

Answer

Since the two are given as mutually exclusive events, by definition, they never occur simultaneously. And since they can never occur together, the probabilty that both A and B happen is 0.

It is easier to visualise the probability spaces of A and B to be two mutually exclusive sets and thus the intersection of A and B is a null set, leading to a probability of 0

Answer

Since A and B are mutually exclusive events, they do not occur together at all.
Hence, the required probability is zero.

Answer

Probability of Mutually Exclusive Events

Two events are considered mutually exclusive if they cannot occur simultaneously. In other words, if one event happens, the other event cannot happen at the same time.

Given that events A and B are mutually exclusive, we need to find the probability of their occurrence together.

Probability of Event A
P(A) = 2/3

This means that the probability of event A occurring is 2/3 or 66.67%.

Probability of Event B
P(B) = 4/9

This means that the probability of event B occurring is 4/9 or approximately 44.44%.

Explanation

Since events A and B are mutually exclusive, they cannot occur at the same time. This means that the intersection of events A and B is an empty set, or in other words, there are no outcomes that satisfy both events simultaneously.

Therefore, the probability of the occurrence of A and B together is 0.

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