Question

1. students were asked what they are allergic to. the table shows the results. if a student is chosen at random, what is the probability that they: probability = \\(\frac{13}{45}\\) 7d are also allergic to dairy given that they are allergic to nuts? probability = \\(\frac{17}{17 + 28}\\) explain probability = enter your next step here

Explanation:

Step1: Recall Conditional Probability

For conditional probability \( P(A|B) \), it's the number of outcomes where both \( A \) and \( B \) occur divided by the number of outcomes where \( B \) occurs. Here, \( A \) is "allergic to dairy" and \( B \) is "allergic to nuts".

Step2: Calculate Denominator

The number of students allergic to nuts is the sum of those allergic to nuts and dairy (\( 17 \)) and those allergic to nuts but not dairy (\( 28 \)), so total for \( B \) is \( 17 + 28 \).

Step3: Calculate Probability

The number of students allergic to both nuts and dairy is \( 17 \). So \( P(\text{dairy}|\text{nuts})=\frac{17}{17 + 28}=\frac{17}{45} \).

Answer:

\(\frac{17}{45}\)