Question

Some researchers claim there is an association between taking vitamins and gaining weight. They took a random sample of people living in Boston, Massachusetts, and recorded whether they took vitamins and whether they gained weight. The results are shown in the following two-way table:
Has Gained Weight Has Not Gained Weight
Does not take vitamins 52 19
Takes one vitamin per day 35 49
Takes more than one vitamin per day 72 80


If a person is chosen at random, what is the probability that he or she has gained weight, given that he or she takes more than one vitamin per day?
0.42
0.45
0.47
0.50

Answer 1

Answer:

The probability that he or she has gained weight, given that he or she takes more than one vitamin per day is 0.47

Step-by-step explanation:

                                       Has Gained Weight        Has Not Gained Weight

Does not take vitamins                          52                                   19

Takes one vitamin per day                    35                                   49

Takes more than one vitamin per day 72                                    80

We are supposed to find the probability that he or she has gained weight, given that he or she takes more than one vitamin per day

A= he or she has gained weight

B=he or she takes more than one vitamin per day

$P(A|B)=\frac{P(A \cap B)}{P(B)}$

$A \cap B = 72$

B = 72+80=152

So,$P(A|B)=\frac{72}{152}=0.47$

So, Option C is true

Hence the probability that he or she has gained weight, given that he or she takes more than one vitamin per day is 0.47