Suppose that in a certain country, the probability of having red hair is 0.20, a

Question

Suppose that in a certain country, the probability of having red hair is 0.20, and the probability of having blue eyes is 0.10. The probability of having both characteristics is 0.02. The probabilities are shown in the Venn diagram, where A is the event that a randomly chosen inhabitant of this country has red hair, and B is the event that a randomly chosen inhabitant has blue eyes A not B 0.18 Both 0.02 B not A 0.08 A 0.20 B=0.10 Scroll Calculate the conditional probability of a person having blue eyes given that he or she has red hair, and us determine whether having blue eyes and red hair are independent. P(B | A) =

Explanation / Answer

P(having blue eyes | having red hair) = P(B | A)

P(B | A) = P(A and B)/P(A)

P(A and B) = 0.02

P(A) = 0.2

So, P(B | A) = 0.02/0.2 = 0.1

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