Answer:
B. P(weight is 120 lb.|consumes 2,000−2,500 calories) ≠ P(weight is 120 lb.)
Step-by-step explanation:
The probability that a person consumes between 1000 and 1500 calories given that the person weighs 165 is found by first finding the number of people weighing 165 that consume between 1000 and 1500 calories. There are 15 people in that category. The probability will be out of the total number of people that weigh 165; this is 117. This makes the probability 15/117 = 0.128.
The probability that someone consumes between 1000 and 1500 calories is given by first finding the number of people that consume that many calories. This number is 140. The probability will be out of the total number of people; this is 500. This makes the probability 140/500 = 0.28.
Since these are not the same, A is not true.
The probability that someone weighs 120 given that they consume between 2000 and 2500 calories is found by first finding the number of people weighing 120 that consume between 2000 and 2500 calories. There are 10 people in that category. The probability will be out of the total number of people that consume between 2000 and 2500 calories; this is 110. This makes the probability 10/110 = 0.09.
The probability that someone weighs 120 pounds is given by first finding the number of people that weigh 120 pounds. This is 180. The probability will be out of the total number of people; this is 500. This makes the probability 180/500 = 0.36.
Since these are not the same, B is true.
The probability that someone weighs 165 given that they consume between 1000 and 2000 calories is found by first finding the number of people weighing 165 that consume between 1000 and 2000 calories. There are 15+27 = 42 people in that category. The probability will be out of the total number of people that consume between 1000 and 2000 calories; this is 140+250 = 390. This makes the probability 42/390 = 0.108.
The probability that someone weighs 165 pounds is given by first finding the number of people that weigh 165 pounds. This is 117. The probability will be out of the total number of people; this is 500. This makes the probability 117/500 = 0.234.
Since these are not the same, C is not true.
The probability that someone weighs 145 given that they consume between 1000 and 2000 calories is found by first finding the number of people weighing 145 that consume between 1000 and 2000 calories. There are 35+143 = 178 people in that category. The probability will be out of the total number of people that consume between 1000 and 2000 calories; this is 140+250 = 390. This makes the probability 178/390 = 0.456.
The probability that someone consumes between 1000 and 2000 calories is given by first finding the number of people that consume between 1000 and 2000 calories. This is 140+250 = 390. The probability will be out of the total number of people; this is 500. This makes the probability 390/500 = 0.78.
Since these are not the same, D is not true.
which simplifies to 
