Sure, let's break it down:

1. The probability that exactly one of the events A or B occurs can be written as P(A or B) - P(A and B). This is because P(A or B) includes the cases where both A and B occur, so we subtract P(A and B) to exclude this case.

2. The probability of either A or B occurring, P(A or B), can be written as P(A) + P(B) - P(A and B) according to the principle of inclusion and exclusion. This is because P(A) + P(B) counts the case where both A and B occur twice, so we subtract P(A and B) to correct this.

3. Substituting the expression from step 2 into the equation from step 1, we get P(A) + P(B) - P(A and B) - P(A and B) = P(A) + P(B) - 2P(A and B).

So, the probability that exactly one of the events A or B occurs is P(A) + P(B) - 2P(A and B).

Question

Sure, let's break it down:

1. The probability that exactly one of the events A or B occurs can be written as P(A or B) - P(A and B). This is because P(A or B) includes the cases where both A and B occur, so we subtract P(A and B) to exclude this case.

2. The probability of either A or B occurring, P(A or B), can be written as P(A) + P(B) - P(A and B) according to the principle of inclusion and exclusion. This is because P(A) + P(B) counts the case where both A and B occur twice, so we subtract P(A and B) to correct this.

3. Substituting the expression from step 2 into the equation from step 1, we get P(A) + P(B) - P(A and B) - P(A and B) = P(A) + P(B) - 2P(A and B).

So, the probability that exactly one of the events A or B occurs is P(A) + P(B) - 2P(A and B).

Knowee AI · Accepted Answer

Sure, let's break it down:

1. The probability that exactly one of the events A or B occurs can be written as P(A or B) - P(A and B). This is because P(A or B) includes the cases where both A and B occur, so we subtract P(A and B) to exclude this case.

2. The probability of either A or B occurring, P(A or B), can be written as P(A) + P(B) - P(A and B) according to the principle of inclusion and exclusion. This is because P(A) + P(B) counts the case where both A and B occur twice, so we subtract P(A and B) to correct this.

3. Substituting the expression from step 2 into the equation from step 1, we get P(A) + P(B) - P(A and B) - P(A and B) = P(A) + P(B) - 2P(A and B).

So, the probability that exactly one of the events A or B occurs is P(A) + P(B) - 2P(A and B).

Show that the probability that exactly one of the events A and B occurs isP(A) + P(B) − 2P(AB).

Question

Show that the probability that exactly one of the events A and B occurs is

Solution

Similar Questions

Upgrade your grade with Knowee