Use the table to answer the question.

Question

Outcome 1 Outcome 2 Outcome 3 TOTAL
Outcome X 4 9 2 15
Outcome Y 6 4 5 15
TOTAL 10 13 7 30
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)
?

(1 point)
Responses

13
13

10
10

15
15

30
30
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Answer 1

To find the probability of Outcome Y given that Outcome 2 occurs (P(Y|Outcome 2)), we can use the formula:

\[ P(A|B) = \frac{n(A \text{ and } B)}{n(B)} \]

In this case, A is Outcome Y, and B is Outcome 2.

1. n(A and B): This is the number of occurrences of Outcome Y when Outcome 2 occurs. From the table, we see that the number corresponding to Outcome Y and Outcome 2 is 4.

2. n(B): This is the total number of occurrences of Outcome 2, which can be found from the bottom row of the table. The total for Outcome 2 is 13.

Therefore, the number you would use in the denominator of your fraction when using the formula to find P(Y|Outcome 2) is 13.

So, the correct answer is:

13