If 30% of students in a physics class also take a calculus course & further assume that P(“earn A in physics”|”taking calculus”) = .4, P(“earn A in physics”|”not taking calculus”) = .1 If a student earns an A in physics what is the probability said student is taking calculus?
Probability course question
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probability
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0I think it is ${12\over19}\approx0.631$. Anon did a good job below. – 2012-10-01
1 Answers
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$C$ = "taking calculus"
$C^c$ = "not taking calculus"
$A$ = "earns A in physics"
You want to find $P(C|A)$
Bayes' Theorem = $P(C|A)$ = $\dfrac{P(A|C)P(C)}{P(A)}$
Law of Total Probability: $P(A)$ = $P(A|C)P(C) + P(A|C^c)P(C^c)$
$P(C)$ = .3
$P(C^c)$ = .7
$P(A|C)$ = .4
$P(A|C^c)$ = .1
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0I got 0.63157894736. Just wanted to see if you would please work thru so I can compare my answer to yours – 2012-10-01