In a particular community, 70% of the voters are Democrats, and 30% are Republicans. Sixty percent of the Democratic voters and 40% of Republican voters favor the incumbent. What is the probability that a randomly selected voter from this community favors the incumbent?

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joaobezerra joaobezerra · Answer 1 · 2020-02-07T22:24:57+01:00

Answer:

There is a 54% probability that a randomly selected voter from this community favors the incumbent.

Step-by-step explanation:

We have these following probabilities:

A 70% probability that a voter is Democrat

A 30% probability that a voter is Republican

A 60% probability that a Democrat voter favors the incumbent.

A 40% probability that a Republican voter favors the incumbent.

What is the probability that a randomly selected voter from this community favors the incumbent?

If the voter is a Democrat, this probability is 60%. 70% of the voters are Democrats.

If the voter is a Republican, this probability is 40%. 30% of the voters are republican. So

[tex]P = 0.6*0.7 + 0.4*0.3 = 0.54[/tex]

There is a 54% probability that a randomly selected voter from this community favors the incumbent.