Question

What is the probability that either event will occur?

12
8
A
3
B
10
A
P(A or B)=P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.

Answer 1

To find the probability of either event A or event B occurring, where A is the event of getting a number greater than 12 and B is the event of getting a number greater than 8, we use the formula P(A or B) = P(A) + P(B) - P(A and B). In this case, P(A or B) equates to 0.8 when rounded to the nearest hundredth.

Step-by-step explanation:

To calculate the probability that either event A or event B will occur, given that A is the event of getting a number greater than 12 and B is the event of getting a number greater than 8, we need to use the provided formula:

P(A or B) = P(A) + P(B) - P(A and B)

We also know that if A and B are mutually exclusive, then P(A and B) = 0. However, since event A is a subset of event B, they are not mutually exclusive, and so we wouldn't assign 0 as the probability for P(A and B).

Instead, we recognize that P(A and B) is essentially P(A), because all outcomes that are greater than 12 are also greater than 8. Hence, as given, P(A) = 3/10. Since all A's are included in B, P(A and B) equals P(A), which means:

P(A and B) = P(A) = 3/10

To find P(A or B), we plug in the values:

P(A or B) = P(A) + P(B) - P(A and B) = 3/10 + 8/10 - 3/10 = 8/10 or 0.8 when converted to decimal and rounded to the nearest hundredth.