The failure rate for taking the bar exam in Philadelphia is 40%. Ifa sample of 1

Question

The failure rate for taking the bar exam in Philadelphia is 40%. Ifa sample of 12 people who have taken the bar exam is selected, whatis the probability? a) At least 2 people passed the exam. b) Exactly 3 people have failed the exam (use binomialformula). c) At least 10 people have failed. a) At least 2 people passed the exam. b) Exactly 3 people have failed the exam (use binomialformula). c) At least 10 people have failed.

Explanation / Answer

Let X be the number of people pass the exam X~Binomial (n = 12, p = 0.6) Binomial formula (X = a) = nCa pa(1-p)n-a a) P(X >=2) = 1 - P( X = 0) - P(X = 1) = 1 - 0.00002 - 0.0003 =0.9997 b) Exactly 3 people fail means that exactly 9 people pass P(X = 9) = 12C9 (0.6)9(0.4)3 = 0.1419 c) At least 10 people fail means that at most 2 people pass P(X

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