SOLUTION: In a school 70 percent have math class 65 percent have science class and 45 percent have math and science what's the probability that a random selected student will have science th

Question 1035080: In a school 70 percent have math class 65 percent have science class and 45 percent have math and science what's the probability that a random selected student will have science this semester given they already have a math class this semester
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p(a given b) = p(a and b) / p(b)

p(a) = probability student takes a math class.
p(b) = probability student takes a science class.
p(a and b) = probability student takes both a math class and a science class.

since 70% take math, then p(a) = .70
since 65% take science, then p(b) = .65
since 45% take both, then p(a and b) = .45

p(a given b) becomes .45 / .70 = .6428571429.

that's the probability that a randomly selected student will take science given that he takes math.

assume 45 students take math and science.
assume 25 students take math only.
assume 20 students take science only.

total number of students is 90 that take either math or science.

out of that 90, 70 take either math or math and science.
that's 25 for math only and 45 that take math and science.
so, out of the 70 who take math, 45 also take science.
that'a a percentage of 45/70 = .6428571429 = approximately 64.29%.

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