Suppose that 40% of Lakehead students have brown hair, 10% have red hair and $0%

Question

Suppose that 40% of Lakehead students have brown hair, 10% have red hair and $0% have hair of some other colour. As it happens, 20% of those with brown hair, 30% of those with red hair and 15% of those with hair of other colours are kleptomaniacs. (a) Find the probability that a randomly selected student is a kleptomaniac. (b) Given that a randomly selected student is a kleptomaniac, find the probability that that student has red hair. (c) Given that a randomly selected student is not a kleptomaniac, find the probability that that student does not have red hair.

Explanation / Answer

P (R ) =0.1 , P (B) = 0.4 P, (Other) = 0.5

P (K/R) = 0.3 ,P(K/B) = 0.2, P(K/Other) = 0.15

1)P(K)= P(R)*P(K/R) + P(K)* P(K/b) + P(K/OTHRER)*P(OTHER)= 0.1*0.3 +.4*.2 +.5*.15 = 0.195

2) P(R/K) =  P(R)*P(K/R) /P(K) = 0.03 / 0.195 =0.1538

3)P(Not K ) = 1-P(K) = 0.805

P(R/NotK) =P(R) * P(Not K/ R) / P(Not K) = 0.1 *(1-0.3) / 0.805 = 0.07/0.805 =0.086

P(Not R/ Not K) = 1 - P(R/NotK) = 1 -0.086 = 0.913

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