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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:

\begin{tabular}{|l|l|l|}
\hline & Has Gained Weight & Has Not Gained Weight \\
\hline Does not take vitamins & 52 & 19 \\
\hline Takes one vitamin per day & 35 & 49 \\
\hline Takes more than one vitamin per day & 72 & 80 \\
\hline
\end{tabular}

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?

A. 0.42
B. 0.45
C. 0.47
D. 0.50



Answer :

GinnyAnswer
To determine the probability that a person has gained weight given that they take more than one vitamin per day, we proceed with the following steps:

1. Identify the relevant data from the table:
- Number of people who take more than one vitamin per day and have gained weight: 72
- Number of people who take more than one vitamin per day and have not gained weight: 80

2. Calculate the total number of people who take more than one vitamin per day:
- Total = Number who have gained weight + Number who have not gained weight
- Total = 72 (gained weight) + 80 (not gained weight) = 152 people

3. Calculate the probability that a person has gained weight given that they take more than one vitamin per day. This is done by dividing the number of people who have gained weight by the total number of people who take more than one vitamin per day:
- Probability = Number who have gained weight / Total number who take more than one vitamin per day
- Probability = 72 / 152

4. Simplify the fraction to obtain:
- Probability ≈ 0.4737

Thus, the probability that a person has gained weight, given that they take more than one vitamin per day, is approximately 0.47.

The closest answer choice is:
- 0.47

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