In a certain year, the u. s. senate was made up of 53 democrats, 45 republicans, and 2 independents who caucus with the democrats. in a survey of the u. s. senate conducted at that time, every senator was asked whether he or she owned at least one gun. of the democrats, 19 declared themselves gun owners; of the republicans, 21 of them declared themselves gun owners; none of the independents owned guns. 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? (round your answer to four decimal places.)

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:

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:

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:

is the probability that the chosen senators is a Democrat. There are 100 total senators, 53 of which are Democrats, so:

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?

There is a 47.50% probability that the chosen senator is a Democrat.

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step-by-step explanation: