Respuesta :
Answer:
a) [tex] P(A \cup B) = P(A) +P(B) - P(A\cap B)[/tex]
And if we solve for [tex] P(A \cap B)[/tex] we got:
[tex] P(A \cap B) = P(A) + P(B) -P(A\cup B)= 0.7+0.3-0.9 = 0.1[/tex]
b) False
The reason is because we don't satisfy the following relationship:
[tex] P(A\cup B) = P(A) + P(B)[/tex]
We have that:
[tex] 0.9 \neq 0.3+0.7 =1[/tex]
c) False
In order to satisfy independence we need to have the following condition:
[tex] P(A \cap B) = P(A) *P(B)[/tex]
And for this case we don't satisfy this relation since:
[tex] 0.1 \neq 0.7*0.3 = 0.21[/tex]
Step-by-step explanation:
For this case we have the following probabilities given:
[tex] P(A) = 0.7, P(B) =0.7, P(A \cup B) =0.9[/tex]
Part a
We want to calculate the following probability: [tex] P(A \cap B)[/tex]
And we can use the total probability rule given by:
[tex] P(A \cup B) = P(A) +P(B) - P(A\cap B)[/tex]
And if we solve for [tex] P(A \cap B)[/tex] we got:
[tex] P(A \cap B) = P(A) + P(B) -P(A\cup B)= 0.7+0.3-0.9 = 0.1[/tex]
Part b
False
The reason is because we don't satisfy the following relationship:
[tex] P(A\cup B) = P(A) + P(B)[/tex]
We have that:
[tex] 0.9 \neq 0.3+0.7 =1[/tex]
Part c
False
In order to satisfy independence we need to have the following condition:
[tex] P(A \cap B) = P(A) *P(B)[/tex]
And for this case we don't satisfy this relation since:
[tex] 0.1 \neq 0.7*0.3 = 0.21[/tex]
