Question

Suppose the probability of an adult male being more than
6 feet tall is 20%, the probability of an adult male having both biological parents of above
average height is 10%, and the probability of an adult male having both biological parents
of above average height is 40% given that the adult male is more than 6 feet tall. What is
the probability that an adult male is more than 6 feet tall given that both of his biological
parents are of above average height? Please simplify your answer to a decimal value and
circle your answer. Ensure you show your work

Answer 1

The inforrmations provided from the question:

P[ height of an adult male being more than 6 feet] =0.2

P[an adult male having both biological parents of above average height]=0.1

P[ an adult male having both biological parents of above average height | adult male is more than 6 feet tall]= 0.4

So, P[ adult male is more than 6 feet tall | both of his biological parents are of above average height]

= P[ an adult male having both biological parents of above average height | adult male is more than 6 feet tall]*P[adult male is more than 6 feet tall]/ P[an adult male having both biological parents of above average height]

[by Bayes' Theorem, P[A|B]=P[A and B]/P[B]=P[B|A]*P[A]/P[B] ]

= 0.4*0.2/0.1=0.8 [answer]