DJHJA wrote:A group of 20 voters composed of 10 democrats and 10 republicans. There are 11 women and 9 men in the group. Seven of the women are democrats. What are the chances of picking a male republican if you pick a voter at random from the group?

a. 1/9

b. 1/5

c.1/4

d. 7/20

e. 9/20

Can anyone help?

I did this with the help of a Table

The answer that i am getting is 6/20, or 3/10, but it there in your options, I don't see any problem with my approach
Share your view

the answer given is 5/20=1/4

i also got 6/20. not sure y they gave 5/20=1/4 as the answer....

Great work, goyalsau:

These "multiple categories" problems are great exercises in staying organized with information. Here, if you break down what you know:

10 democrats, 10 republicans
11 women, 9 men
7 women democrats --> the other 4 women are republicans
4 women republicans --> the other 6 republicans are men

6 male republicans / 20 total people = 6/20 or 3/10 chance of picking a male republican.


One helpful strategy in problem solving is to "follow the data" - use what you know to solve for the next unknown, and you'll follow a path toward filling in all the blanks.


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One other note: someone posted on this board today that they were having trouble with probability in general. I'd argue that at least 1/3 of "probability" questions aren't probability questions at all - they're, like this one, problems in which your final answer is EXPRESSED as a probability, but really they're arithmetic/algebra problems that simply require as a final step your knowledge that:


Probability of A = # of A outcomes / # of total outcomes

As long as you know the number of total outcomes and the number of those that get you what you want, you just have to express your answer as a fraction and the whole thing is solved.

thanks