Question

in a large school, it was found that 70% of students are taking a math class, 74% of student are taking an english class, and 59% 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 of two events

The formula is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $P(A)$ is the probability of event $A$, $P(B)$ is the probability of event $B$, and $P(A\cap B)$ is the probability of both $A$ and $B$ occurring. 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 are given $P(A) = 0.7$, $P(B)=0.74$, and $P(A\cap B)=0.59$.

Step2: Substitute the values into the formula

$P(A\cup B)=0.7 + 0.74-0.59$.

Step3: Calculate the result

$P(A\cup B)=0.85$.

Answer:

$0.85$