Question

If the probability of a student taking a calculus class is 0.10, the probability of taking a statistics class is 0.90, and the probability of taking a calculus class and a statistics class is 0.07, what is the probability of a student taking a calculus class or a statistics class

Answer 1

Answer:

93% probability of a student taking a calculus class or a statistics class

Step-by-step explanation:

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a student takes a calculus class.

B is the probability that a student takes a statistics class.

We have that:

$A = a + (A \cap B)$

In which a is the probability that a student takes calculus but not statistics and $A \cap B$ is the probability that a student takes both these classes.

By the same logic, we have that:

$B = b + (A \cap B)$

The probability of taking a calculus class and a statistics class is 0.07

This means that $A \cap B = 0.07$

The probability of taking a statistics class is 0.90

This means that $B = 0.9$. So

$B = b + (A \cap B)$

$0.9 = b + 0.07$

$b = 0.83$

The probability of a student taking a calculus class is 0.10

This means that $A = 0.1$

$A = a + (A \cap B)$

$0.1 = a + 0.07$

$a = 0.03$

What is the probability of a student taking a calculus class or a statistics class

$A \cup B = a + b + A \cap B = 0.03 + 0.83 + 0.07 = 0.93$

93% probability of a student taking a calculus class or a statistics class