Question

The probability of events A

and B
is

P(A)=1/2

P(B)=1/3

P(A∩B)=1/4.

What is the value of P(A or B)?
Enter your answer as a fraction, like this: 4/25

Note: I know the answer is NOT 2/3.

Answer 1

The probability of event A or event B occurring, P(A OR B), is calculated as the sum of the probabilities of A and B minus the probability of A and B occurring together, resulting in 7/12.

Step-by-step explanation:

The probability of either event A or event B occurring is given by the addition rule, which states that P(A OR B) = P(A) + P(B) − P(A AND B). To find P(A OR B), we simply add the probabilities of A and B and then subtract the probability of A and B occurring together.

In this case:

P(A) = 1/2,
P(B) = 1/3, and
P(A AND B) = 1/4.

Thus, P(A OR B) = (1/2) + (1/3) - (1/4).

To add fractions, we need a common denominator, which in this case is 12, resulting in:

P(A OR B) = (6/12) + (4/12) - (3/12) = (6+4-3)/12 = 7/12.

Therefore, the value of P(A OR B) is 7/12.