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) =

1 answer

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:

\[ \boxed{35} \]