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Suppose that a certain college class contains 35 students. of these, 17 are juniors, 20 are social science majors, and 12 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 social science major? (b) given that the student selected is a junior, what is the probability that she is also a social science major?

Respuesta :

LammettHash
a) Suppose [tex]J[/tex] is the set of juniors and [tex]S[/tex] is the set of social science majors. There are 35 students in all, but 12 of them don't belong to either set, so [tex]|J\cup S|=35-12=23[/tex]. Then

[tex]|J\cap S|=|J|+|S|-|J\cup S|=17+20-23=14[/tex]

So the probability that a random student is both a junior and social science major is [tex]\mathbb P(J\cap S)=\dfrac{14}{35}[/tex]

b) We're looking for the probability [tex]\mathbb P(S\mid J)[/tex]. By definition, this would be


[tex]\mathbb P(S\mid J)=\dfrac{\mathbb P(S\cap J)}{\mathbb P(J)}=\dfrac{\frac{14}{35}}{\frac{17}{35}}=\dfrac{14}{17}[/tex]
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