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Use the table to answer the question. Various Outcomes of Different Types of Events 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 15 15 13 13

1 answer

To find the probability of Outcome Y given that Outcome 2 occurs, we need to understand the notation used in the formula P(A|B) = n(A and B) / n(B).

In this case:

  • Event A is Outcome Y.
  • Event B is Outcome 2.

To compute P(Y|Outcome 2), we need:

  1. n(A and B): the number of occurrences where both Outcome Y and Outcome 2 happen. From the table, this value is 4 (the intersection of Outcome Y and Outcome 2).
  2. n(B): the total number of outcomes when Outcome 2 occurs. We need to sum the counts of both Outcome X and Outcome Y for Outcome 2 from the table, which is 9 (from Outcome X) + 4 (from Outcome Y) = 13.

So, the number you would use in the denominator n(B) when calculating P(Y|Outcome 2) is 13.

The correct response is: 13