What is the probability of A and B if A and B are mutually exclusive?

What is the probability of A and B if A and B are mutually exclusive?

If Events A and B are mutually exclusive, P(A ∩ B) = 0. The probability that Events A or B occur is the probability of the union of A and B. The probability of the union of Events A and B is denoted by P(A ∪ B) .

When A and B are mutually exclusive events?

A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0. For example, suppose the sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

When two events are mutually exclusive Why is P A and B )= 0?

If two events have no elements in common (Their intersection is the empty set.), the events are called mutually exclusive. Thus, P(A∩B)=0 . This means that the probability of event A and event B happening is zero. They cannot both happen.

For what value of P B are A and B mutually exclusive?

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If P(A AND B) = 0, then A and B are mutually exclusive.)

What is the probability of an intersection of two mutually exclusive events?

Therefore, for the intersection of mutually exclusive events A i with i ∈ { 1, …, n | n ∈ N ∖ { 1 } } holds ⋂ 1 n A i = ∅. This implies P [ ⋂ 1 n A i] = P [ ∅] = 0. In general, the probability of the union of two events is P [ B ⋃ C] = P [ B] + P [ C] − P [ B ⋂ C] . Hence, for mutually exclusive events holds P [ ⋃ 1 n A i] = ∑ 1 n P [ A i].

What does it mean to have mutually exclusive events?

To have mutually exclusive events means if one of those events occurs, the others cannot occur. Therefore, for the intersection of mutually exclusive events A i with i ∈ { 1, …, n | n ∈ N ∖ { 1 } } holds ⋂ 1 n A i = ∅.

Which is the probability of the Union of two events?

This implies P [ ⋂ 1 n A i] = P [ ∅] = 0. In general, the probability of the union of two events is P [ B ⋃ C] = P [ B] + P [ C] − P [ B ⋂ C] . Hence, for mutually exclusive events holds P [ ⋃ 1 n A i] = ∑ 1 n P [ A i]. Knowing this, you can apply it to your tasks:

What is the probability that A and B occur?

Suppose that A and B are mutually exclusive events for which P ( A) = 0.3 and P ( B) = 0.5. What is the probability that (a) either A or B occurs?