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
Based on the calculations, the probability of a U.S. adult being obese is 0.537, or 53.7% (rounded to three decimals).
Now, let's determine whether a U.S. adult who is obese is more likely to be male or female.
To calculate this, we will use conditional probability. We need to find the probability of being male given that the person is obese (P(Male|Obese)) and the probability of being female given that the person is obese (P(Female|Obese)).
P(Male|Obese) = P(Male and Obese) / P(Obese) = 0.101 / 0.537 = 0.188 or 18.8% (rounded to three decimals).
P(Female|Obese) = P(Female and Obese) / P(Obese) = 0.101 / 0.537 = 0.188 or 18.8% (rounded to three decimals).
Based on these calculations, if a U.S. adult is obese, there is an almost equal probability of them being male or female (approximately 18.8% for both genders). Therefore, we cannot make a definitive conclusion about their gender based solely on the fact that they are obese.