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Use the table to answer the 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

15
15

13
13

10
10

30
30

1 answer

To find the probability of Outcome Y given that Outcome 2 occurs, we use the formula for conditional probability \( P(A|B) = \frac{n(A \text{ and } B)}{n(B)} \).

In this context:

  • \( A \) is "Outcome Y"
  • \( B \) is "Outcome 2"

The denominator \( n(B) \) is the total number of occurrences of Outcome 2. From the table, we can see that the total occurrences for Outcome 2 (across all events) is 13.

Thus, the number you would use in the denominator of your fraction is 13.