SOLUTION: Intersection and conditional probability Suppose that a certain college class contains 64 students. Of these,35 are juniors, 34 are history majors, and 9 are neither. A student

Question 349170: Intersection and conditional probability
Suppose that a certain college class contains 64 students. Of these,35 are juniors, 34 are history majors, and 9 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a junior and a history major?
(b) Given that the student selected is a history major, what is the probability that she is also a junior?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Intersection and conditional probability
Suppose that a certain college class contains 64 students. Of these,35 are juniors, 34 are history majors, and 9 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a junior and a history major?
p(jun AND hm) = 24/45
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(b) Given that the student selected is a history major, what is the probability that she is also a junior?
P(j|hm) = 24/34
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Draw a Venn diagram with two intersecting circles: j and hm
Procedure
The number of students in j+(j AND hm)+ hm = 45 - (j AND hm)
Let # in (j AND hm) = x
Then # if j but not in j AND m = 35-x
And # in hm but not in j AND m = 34-x
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Solve for "x".
I get x = 24
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From that you can figure out the propabilities.
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Cheers,
Stan H.

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