to get to know her students better, ms. alexander surveyed her math students to determine what hobbies and…

to get to know her students better, ms. alexander surveyed her math students to determine what hobbies and school subjects they prefer.\n| |athletics|the arts|\n|--|--|--|\n|math|1|2|\n|literature|3|4|\nwhat is the probability that a randomly selected student prefers math or prefers athletics?\nsimplify any fractions.

to get to know her students better, ms. alexander surveyed her math students to determine what hobbies and school subjects they prefer.\n| |athletics|the arts|\n|--|--|--|\n|math|1|2|\n|literature|3|4|\nwhat is the probability that a randomly selected student prefers math or prefers athletics?\nsimplify any fractions.

Answer

Explanation:

Step1: Calculate total number of students

$1 + 2+3 + 4=10$

Step2: Calculate number of students who prefer math

$1 + 2 = 3$

Step3: Calculate number of students who prefer athletics

$1+3 = 4$

Step4: Calculate number of students who prefer both math and athletics

$1$

Step5: Use the formula for $P(A\cup B)$

$P(\text{math}\cup\text{athletics})=\frac{n(\text{math})+n(\text{athletics})-n(\text{math}\cap\text{athletics})}{n(\text{total})}=\frac{3 + 4-1}{10}=\frac{6}{10}=\frac{3}{5}$

Answer:

$\frac{3}{5}$