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Answered

A researcher surveyed 1500 people to determine if nut and milk allergies are related. The survey results are summarized in the table below.

| | Allergic to Nuts | Not Allergic to Nuts |
|---------------|-------------------|----------------------|
| Allergic to Milk | 3 | 42 |
| Not Allergic to Milk | 12 | 1443 |

Determine the probability that a randomly selected survey respondent is allergic to milk.



Answer :

To determine the probability that a randomly selected survey respondent is allergic to milk, we need to follow these steps:

1. Identify the total number of surveyed people:
The total number of people surveyed is 1500.

2. Identify the number of people who are allergic to milk:
To find this, we need to look at everyone who has a milk allergy, regardless of whether they are allergic to nuts or not. From the table, we can see:
- There are 3 people who are allergic to both nuts and milk.
- There are 42 people who are allergic to milk but not nuts.

Therefore, the total number of people who are allergic to milk is:
[tex]\[ 3 + 42 = 45 \][/tex]

3. Calculate the probability:
The probability is found by dividing the number of people who are allergic to milk by the total number of people surveyed. So, the probability [tex]\(P\)[/tex] that a randomly selected survey respondent is allergic to milk is:
[tex]\[ P(\text{Allergic to Milk}) = \frac{\text{Number of people allergic to milk}}{\text{Total number of people surveyed}} \][/tex]

Substituting the numbers:
[tex]\[ P(\text{Allergic to Milk}) = \frac{45}{1500} \][/tex]

Simplifying this fraction:
[tex]\[ P(\text{Allergic to Milk}) = 0.03 \][/tex]

Therefore, the probability that a randomly selected survey respondent is allergic to milk is [tex]\(0.03\)[/tex] or [tex]\(3\%\)[/tex].