Subjects statistics

Conditional Probability 8B8Fb5

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1. **State the problem:** We want to find the probability that a randomly chosen student prefers pizza given that the student is female. 2. **Identify the formula:** The conditional probability formula is $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ where $A$ is the event "prefers pizza" and $B$ is the event "is female". 3. **Extract data from the table:** - Number of females who prefer pizza: 119 - Total number of females: $219 + 192 + 119 = 530$ 4. **Calculate the conditional probability:** $$P(\text{pizza} | \text{female}) = \frac{119}{530}$$ 5. **Simplify the fraction:** $$\frac{119}{530} = \frac{\cancel{119}}{\cancel{530}} \approx 0.2245$$ 6. **Convert to percentage and round:** $$0.2245 \times 100 = 22.45\% \approx 22.5\%$$ **Final answer:** The probability that a randomly chosen female student prefers pizza is approximately **22.5%**.