Question

In a large school, it was found that 77% of students are taking a math class, 74% of student are taking an English class, and 70% 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. Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.

Answer 1

Answer:

0.81 = 81% probability that a randomly selected student is taking a math class or an English class.

0.19 = 19% probability that a randomly selected student is taking neither a math class nor an English class

Step-by-step explanation:

We solve this question working with the probabilities as Venn sets.

I am going to say that:

Event A: Taking a math class.

Event B: Taking an English class.

77% of students are taking a math class

This means that $P(A) = 0.77$

74% of student are taking an English class

This means that $P(B) = 0.74$

70% of students are taking both

This means that $P(A \cap B) = 0.7$

Find the probability that a randomly selected student is taking a math class or an English class.

This is $P(A \cup B)$, which is given by:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

So

$P(A \cup B) = 0.77 + 0.74 - 0.7 = 0.81$

0.81 = 81% probability that a randomly selected student is taking a math class or an English class.

Find the probability that a randomly selected student is taking neither a math class nor an English class.

This is

$1 - P(A \cup B) = 1 - 0.81 = 0.19$

0.19 = 19% probability that a randomly selected student is taking neither a math class nor an English class