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?

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26-04-2018
Mathematics

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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?

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LammettHash LammettHash · Answer 1 · 2018-04-27T00:12:44+02:00

LammettHash LammettHash

27-04-2018

By definition of conditional probability,

[tex]\mathbb P(\text{history}\mid\text{science})=\dfrac{\mathbb P(\text{history AND science})}{\mathbb P(\text{science})}=\dfrac{0.38}{0.78}\approx0.49[/tex]

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