Respuesta :
Answer:
There is a 47.50% probability that the chosen senator is a Democrat.
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula:
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
In your problem we have that:
A(what happened) is the probability of a gun owner being chosen:
There are 100 people in the survay(53 Democrats, 45 Republicans ans 2 Independents), and 40 of them have guns(19 Democrats, 21 Republicans). So, the probability of a gun owner being chosen is:
[tex]P(A) = \frac{40}{100} = 0.4[/tex]
[tex]P(A/B)[/tex] is the probability of a senator owning a gun, given that he is a Democrat. 19 of 53 Democrats own guns, so the probability of a democrat owning a gun is:
[tex]P(A/B) = \frac{19}{53} = 0.3585[/tex]
[tex]P(B)[/tex] is the probability that the chosen senators is a Democrat. There are 100 total senators, 53 of which are Democrats, so:
[tex]P(B) = \frac{53}{100} = 0.53[/tex]
If a senator participating in that survey was picked at random and turned out to be a gun owner, what was the probability that he or she was a Democrat?
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{(0.53)*(0.3585)}{(0.40)} = 0.4750[/tex]
There is a 47.50% probability that the chosen senator is a Democrat.
