Question

At a high school, the probability that a student takes a science class and a history class is 0.38. The probability that a student takes a science class is 0.78, and the probability that the student takes a history class is 0.60. What is the probability (rounded to the nearest hundredth) that a student takes a history class given that the student is taking a science class?

Answer 1

By definition of conditional probability,


`\mathbb P(\text{history}\mid\text{science})=\frac{\mathbb P(\text{history AND science})}{\mathbb P(\text{science})}=(0.38)/(0.78)\approx0.49`