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].
