1. **State the problem:** We want to find the probability that a customer bought premium gas given that they paid with a credit card. 2. **Identify given probabilities:** - $P(\text{Regular})=0.88$, $P(\text{Midgrade})=0.02$, $P(\text{Premium})=0.10$ - $P(\text{Credit} | \text{Regular})=0.28$ - $P(\text{Credit} | \text{Midgrade})=0.34$ - $P(\text{Credit} | \text{Premium})=0.42$ - $P(\text{Credit})=0.295$ 3. **Use Bayes' theorem:** $$ P(\text{Premium} | \text{Credit}) = \frac{P(\text{Credit} | \text{Premium}) \times P(\text{Premium})}{P(\text{Credit})} $$ 4. **Calculate numerator:** $$ P(\text{Credit} | \text{Premium}) \times P(\text{Premium}) = 0.42 \times 0.10 = 0.042 $$ 5. **Calculate denominator:** Given as $P(\text{Credit})=0.295$ 6. **Calculate conditional probability:** $$ P(\text{Premium} | \text{Credit}) = \frac{0.042}{0.295} $$ 7. **Simplify fraction with cancellation:** $$ P(\text{Premium} | \text{Credit}) = \frac{\cancel{0.042}}{\cancel{0.295}} = 0.1424 \approx 0.142 $$ **Final answer:** The probability that a customer bought premium gas given that they paid with a credit card is approximately **0.142**.