Subjects probability

Conditional Probability Bc87Fc

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1. **State the problem:** We have a survey of 150 college students. Among them, 60 subscribe to Netflix, 45 subscribe to Disney+, and 15 subscribe to both Netflix and Disney+. 2. **Find the probability that a person subscribes to Netflix given they subscribe to Disney+.** 3. **Recall the formula for conditional probability:** $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ where $A$ is the event "subscribes to Netflix" and $B$ is the event "subscribes to Disney+". 4. **Calculate the probabilities:** - Total number of students: $150$ - Number subscribing to Netflix: $60$ - Number subscribing to Disney+: $45$ - Number subscribing to both: $15$ 5. **Calculate $P(A \cap B)$:** $$P(A \cap B) = \frac{15}{150} = \frac{1}{10}$$ 6. **Calculate $P(B)$:** $$P(B) = \frac{45}{150} = \frac{3}{10}$$ 7. **Apply the conditional probability formula:** $$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{1}{10}}{\frac{3}{10}} = \frac{1}{10} \times \frac{10}{3} = \frac{1}{3}$$ 8. **Interpretation:** Given that a student subscribes to Disney+, the probability that they also subscribe to Netflix is $\frac{1}{3}$. **Final answer:** $$\boxed{\frac{1}{3}}$$