Question

A game company gave customers one of two games to test and asked whether they would recommend their game. What is the probability that a customer who recommended their game tested Game A? Round to the nearest whole percent.

Game A Game B
Would Recommend 28 52
Would Not Recommend 19 13
P(tested Game A | recommended their game) =

Answer 1

To find the probability that a customer who recommended their game tested Game A, we can use conditional probability.

Let:
- \( R_A \): the event that a customer tested Game A and recommended it.
- \( R_B \): the event that a customer tested Game B and recommended it.
- \( R \): the event that a customer recommended their game.

From the data provided:

- Customers who tested Game A and would recommend it: 28
- Customers who tested Game B and would recommend it: 52

Now we can calculate the total number of customers who recommended their games (the total number of recommenders):

\[
R = R_A + R_B = 28 + 52 = 80
\]

Now, we want to find \( P(tested \, Game \, A \mid recommended \, their \, game) \), which is given by:

\[
P(tested \, Game \, A \mid recommended \, their \, game) = \frac{P(tested \, Game \, A \cap recommended \, their \, game)}{P(recommended \, their \, game)} = \frac{R_A}{R}
\]

Substituting the values we calculated:

\[
P(tested \, Game \, A \mid recommended \, their \, game) = \frac{28}{80}
\]

Now, we can simplify this fraction:

\[
P(tested \, Game \, A \mid recommended \, their \, game) = 0.35
\]

To express this probability as a percentage, we multiply by 100:

\[
0.35 \times 100 = 35\%
\]

Finally, rounding 35% to the nearest whole percent, we get:

\[
\boxed{35}
\]