Question

I need help with 10.13 part a and b

APPLY YOUR KNOWLEDGE 10.13 Eye color, hair color, and freckles. A large study of children of Caucasian descent in Germany looked at the effect of eye color, hair color, and freckles on the reported extent of burning from sun exposure. The population's distribution of hair color,

Answer 1

a)from given diagram

P(Blue eyes |red hair) =0.473 (this is probability that a Caucasian child will have Blue eyes if he/she has red hair)

P(blue eyes and red hair) =P(red hair)*P{blue eyes |Red hair) =0.025*0.473 =0.011825

this is probability that a Caucasian child has both blue eyes and red hair.

b)

P(freckles |red hair and blue eyes) =0.857

(this is probability that a Caucasian child will have freckles if he/she has red hair and blue eyes both)

P(freckles and red hair and blue eyes) =P(red hair and blue eyes)*P(freckles |red hair and blue eyes)

=0.011825*0.857 =0.010103

(this is probability that a Caucasian child has each of freckles, blue eyes and red hair.)