At a high school, the probability that a student takes a science class and a history class is 0.48. the probability that a student takes a science class is 0.82, and the probability that the student takes a history class is 0.64. 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?
a)0.39
b)0.75
c)0.30
d)0.59

Solutions 

Probability: number of favourable outcomes
                   __________________________

                   total number of possible outcomes

In general, the total number of possible outcomes can be determined by multiplying the number of possible outcomes for each event. 

P(A|B)=  

P(A|B) ⇒ P(taking history | taking science) , Therefore A corresponds to taking history, B corresponds to taking science. 

P(A,B) will be the probability that a student is taking both of the subjects. 

P(B) is the probability that a student is taking the subject science                       (regardless of whether he/she takes history or not)

Now to solve the problem you plug in the given numbers. 

0.48 ÷ 0.82

0.48 is the Probability of (A,B) and 0.82 is the Probability of (B) 

= 0.58537 

Rounded to 0.59 

Answer = (D)