to get to know her students better, ms. olson surveyed her math students to determine what hobbies and…
to get to know her students better, ms. olson surveyed her math students to determine what hobbies and school subjects they prefer. math literature athletics 6 6 the arts 4 4 what is the probability that a randomly selected student prefers the arts given that the student prefers math? simplify any fractions.
Answer
Explanation:
Step1: Find number of students who prefer math
The number of students who prefer math is (6 + 4=10).
Step2: Find number of students who prefer both math and the arts
The number of students who prefer both math and the arts is 4.
Step3: Calculate conditional - probability
The formula for conditional probability (P(A|B)=\frac{P(A\cap B)}{P(B)}). In terms of counts, if (A) is the event of preferring the arts and (B) is the event of preferring math, then (P(A|B)=\frac{n(A\cap B)}{n(B)}). Substituting the values we found, we get (\frac{4}{10}=\frac{2}{5}).
Answer:
(\frac{2}{5})