Stats question

Question

in a certain county, 45% of the registered voters are democrats, 35% are republicans, and 20% are independents. sixty percent of the democrats, 80% of the republicans, and 30% of the independents favored increased spending to combat terrorism. If a person chosen at random from the county does not favor increased spending to combat terrorism, what is the probability that the person is a democrat?

Answer 1

45% of all voters are Democrats.  60% of them favor increased spending, so 40% do not.

35% of all voters are Republicans.  80% of them favor increased spending, so 20% do not.

20% of all voters are independents.  30% of them favor increased spending, so 70% do not.

 

18% of all voters (40 * 45) are Democrats who do not favor increased spending.

7% of all voters (20 * 35) are Republicans who do not favor increased spending.

14% of all voters (70 * 20) are independents who do not favor increased spending.

 

So 39% of all voters (18 + 7 + 14) do not favor increased spending.

 

So 46% (18 / 39) of all voters who do not favor increased spending are Democrats.