Respuesta :
Answer:
a. 0.51
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 men is smart.
B is the probability that a men is funny.
C is the probability that a mean is neither of those.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a men is smart but not funny and [tex]A \cap B[/tex] is the probability that a men is both of these things.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
The sum of the probabilities is decimal 1, so:
[tex]a + b + (A \cap B) + C = 1[/tex].
We want to find C. We find the values of each of these probabilities, starting from the intersection.
16% are both smart and funny. This means that [tex]A \cap B = 0.16[/tex]
33% are funny. This means that [tex]B = 0.33[/tex]. So
[tex]B = b + (A \cap B)[/tex]
[tex]0.33= b + 0.16[/tex]
[tex]b = 0.17[/tex].
32% are smart. This means that [tex]A = 0.32[/tex]. So
[tex]A = a + (A \cap B)[/tex]
[tex]0.32= a + 0.16[/tex]
[tex]a = 0.16[/tex].
Now we find C
[tex]a + b + (A \cap B) + C = 1[/tex]
[tex]0.16 + 0.17 + 0.16 + C = 1[/tex]
[tex]0.49 + C = 1[/tex]
[tex]C = 0.51[/tex].
The correct answer is:
a. 0.51
