Outcome X, Outcome 1: 4, Outcome 2 9, Outcome 3 2, otal 15. Outcome Y: Outcome 1 6, Outcome 2 4, Outcome 3 7, Total 15, Total 10, 13, 7, 30

Question

\The table shows the various outcomes of two different events. In order to find the probability of Outcome Y given that Outcome 2 occurs, what number would you use in the denominator of your fraction when using the formula P(A|B)=n(A and B)/n(B) ?

A. 13
B. 10
C. 30
D. 15

Answer 1

To find the probability of Outcome Y given that Outcome 2 occurs, you would use the total number of occurrences of Outcome 2 as the denominator in the probability formula \( P(A|B) = \frac{n(A \text{ and } B)}{n(B)} \).

First, let's summarize the counts from the provided data for Outcome 2:

• For Outcome X, Outcome 2 occurs 9 times.
• For Outcome Y, Outcome 2 occurs 4 times.

Now, the total for Outcome 2 is calculated by adding the counts from both outcomes:

Total for Outcome 2 = 9 (Outcome X) + 4 (Outcome Y) = 13

Thus, \( n(B) \), the total number of occurrences for Outcome 2, would be 13.

So, the number you would use in the denominator of your fraction when calculating \( P(A|B) \) is:

A. 13