Question

section 5.2 homework
score: 7.67/15 answered: 8/15
question 9
in a large school, it was found that 71% of students are taking a math class, 76% of student are taking an english class, and 50% of students are taking both.
find the probability that a randomly selected student is taking a math class or an english class. write your answer as a decimal, and round to 2 decimal places if necessary.

Explanation:

Step1: Recall the formula for the probability of the union

The formula for $P(A\cup B)$ is $P(A)+P(B)-P(A\cap B)$. Let $A$ be the event that a student is taking a math - class and $B$ be the event that a student is taking an English class.
We know that $P(A) = 0.71$, $P(B)=0.76$ and $P(A\cap B)=0.50$.

Step2: Substitute the values into the formula

$P(A\cup B)=P(A)+P(B)-P(A\cap B)=0.71 + 0.76-0.50$.

Step3: Calculate the result

$0.71+0.76 - 0.50=0.97$.

Answer:

$0.97$