In a certain city, 30 percent of the people are conservatives, 50 percent are liberals, and 20 percent are independents. records show that in a particular election, 65 percent of the conservatives voted, 82 percent of the liberals voted, and 50 percent of the independents voted. if a person in the city is selected at random and it is learned that she did not vote in the last election, what is the probability that she is a liberal?

If the person did not vote it can be:
30/100 (30%) people in the city are conservatives, and only 65/100 voted - so 45/100 did not voted.

Liberals are 50% of the city population (1/2), and 82/100 of them voted, so 100/100-82/100=8/100 did not voted!

So let’s make 2 probability events:
1) A person did not voted
2) a person is liberal

Probability that the person is a liberal: 1/2
Person didn’t voted and it’s a liberal:
1/2*8/100= 8/200=4/100 [*]

[*] To count the probability of two probability events you need to multiply them.