Based on recent U.S. Census data of adults, approximately 48% are male. According to a 2013 study by The Henry J. Kaiser Family Foundation, 70% of U.S. adult males are obese while 58% of U.S. adult females are obese (round to THREE decimals).

Question

Based on recent U.S. Census data of adults, approximately 48% are male.   According to a 2013 study by The Henry J. Kaiser Family Foundation, 70% of U.S. adult males are obese while 58% of U.S. adult females are obese (round to THREE decimals).

What is the probability of an U.S. adult being obese?

P (US male and obese)= 0.48 x 0.70 = 0.336
P (US female and obese)= 0.52 x 0.58 = 0.302
P(A∪B)=P(A)+P(B)-P(A∩B)= 0.336+0.302-0.101=0.537

Suppose a U.S. adult is obese. Using probability, would you expect this person to be male or female and why?

P(A|B)= P(A∩B)/P(B) = 0.101/0.302=0.334
P(B|A)=  P(B∩A)/(P(A))=0.101/0.336=0.301