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:
\[ \boxed{35} \]