Question

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 10 10 30 30 13 13 15

Answer 1

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

Here, Event A is Outcome Y, and Event B is the occurrence of Outcome 2.

To identify \( n(B) \), we need the total number of outcomes in which Outcome 2 occurs. From the table, the total number of outcomes for Outcome 2 is found by summing the values in that column:

• For Outcome X at Outcome 2: 9
• For Outcome Y at Outcome 2: 4

Thus, the total number of occurrences for Outcome 2 is: \[ 9 + 4 = 13 \]

Therefore, the denominator \( n(B) \) is \( 13 \).

So, the answer is 13.