40% of all registered voters are Republicans, 45% of all registered voters are Democrats and 15% of all registered voters are Independents. Among the Republican voters, 60% are men. Among the Democratic voters, 30% are men. Finally among the Independent voters, 20% are men.

a. A person is selected at random from the population. What is the probability this person is a man?

b. A person is selected at random from the population and is found to be a woman. What is the probability this person is an Independent?

a) 0.405

b) 0.269

Step-by-step explanation:

a) Let's first find the percentage chance of a voter being a republican AND a man:

0.4 * 0.6 = 0.24

Similarly for democrats that are men: 0.45 * 0.3 = 0.135

And lastly for independent voters that are men: 0.15 * 0.2 = 0.03

To solve this part, we just need to add the percentages we found above. This comes out to be: 0.24 + 0.135 + 0.03 = 0.405

b) To find the probability the person is an independent provided that she is a woman can be found by the following method.

First write down the probability the voter is a republican AND a woman. This is : 0.4 * 0.4 = 0.16

Similarly for democrats that are women: 0.45 * 0.7 = 0.315

And lastly for independent voters that are women: 0.15 * 0.8 = 0.12

To find the probability a voter is independent provided that she is a woman is: 0.16 / (0.16 + 0.315 + 0.12) = 0.269