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: (table: allergic to nuts, not allergic to nuts; allergic to dairy: 17, 19; not allergic to dairy: 28, 26) 7a are allergic to dairy? probability = enter your next step here

Explanation:

Step1: Find total number of students

To find the total number of students, we sum up all the values in the table. The values are 17 (allergic to nuts and dairy), 19 (not allergic to nuts but allergic to dairy), 28 (allergic to nuts but not dairy), and 26 (not allergic to nuts or dairy). So total students = \(17 + 19 + 28 + 26\)
\(17+19 = 36\), \(28 + 26 = 54\), then \(36+54=90\)

Step2: Find number of students allergic to dairy

Students allergic to dairy are those in the "Allergic to dairy" row. So we sum the values in that row: \(17 + 19\)
\(17+19 = 36\)

Step3: Calculate the probability

Probability is the number of favorable outcomes (allergic to dairy) divided by total number of outcomes (total students). So probability = \(\frac{36}{90}\)
Simplify \(\frac{36}{90}\) by dividing numerator and denominator by 18: \(\frac{36\div18}{90\div18}=\frac{2}{5}\)

Answer:

\(\frac{2}{5}\)