4 10 points The following table shows a persons eye color an

4) (10 points) The following table shows a person?s eye color and hair color. a) What is the probability that a randomly selected person has hazel eyes? b) What is the probability that a randomly selected person has green eyes AND red hair? c) What is the probability that a randomly selected person has red hair OR blue eyes? d) Given that a person has blue eyes, what is the probability that a randomly selected person had brown hair?

Solution

a) Prob for hazel eyes = 31/313 = 0.0990

b) Prob for green eyes and red hair = 7/313 = 0.0224

c) Prob for red hair or blue eyes = P(red hair)+P(blue eyes)-P(red hair and blue eyes)

= (37+114-7)/313 = 0.4600

d) P(brown hair/blue eyes) = P(brown hair and blue eyes)/P(Blue eyes)

= 34/114 = 0.298