Respuesta :
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:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a student takes calculus but not statistics and [tex]A \cap B[/tex] is the probability that a student takes both these classes.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
The probability of taking a calculus class and a statistics class is 0.07
This means that [tex]A \cap B = 0.07[/tex]
The probability of taking a statistics class is 0.90
This means that [tex]B = 0.9[/tex]. So
[tex]B = b + (A \cap B)[/tex]
[tex]0.9 = b + 0.07[/tex]
[tex]b = 0.83[/tex]
The probability of a student taking a calculus class is 0.10
This means that [tex]A = 0.1[/tex]
[tex]A = a + (A \cap B)[/tex]
[tex]0.1 = a + 0.07[/tex]
[tex]a = 0.03[/tex]
What is the probability of a student taking a calculus class or a statistics class
[tex]A \cup B = a + b + A \cap B = 0.03 + 0.83 + 0.07 = 0.93[/tex]
93% probability of a student taking a calculus class or a statistics class
