Question

In a survey involving 550 likely Democratic voters and 450 likely Republican voters, the question "Do you support or oppose legislation that would require registration of all handguns?" was asked. The following results were obtained. (POSTING PICTURE)

If a randomly chosen respondent in the survey answered "Oppose" what is the probability tat he or she is a likely Democratic voter?

Answer 1

Results

Answer 2

This is conditional probability. We are given / told that the person chosen at random OPPOSED the legislation in question. That's a CONDITION.

Please count: How many people, TOTAL, opposed this legislation?
Of those, how many were likely Demo. voters?

P(likely Dem voter | voter opposed the legislation) =

No. of likely Demo voters who opposed the legislation
-------------------------------------------------- = ???
Total number of people who opposed the legislation

Answer 3

.1571?

Answer 4

If you don't mind, please share your work with me; I'd like to see how you arrived at your answer. Thanks.

Answer 5

Okay will do

Answer 6

Hope you can read that

Answer 7

@mathmale

Answer 8

thank you for making the effort to share your work.

My opinion is that you don't really need the numbers of voters; just the percentages in the table should be sufficient.

Look at the "oppose" row. You see .25 and .10. Add these together. The resulting sum is the fraction of the whole population who oppose the legislation. What is that fraction?

Now divide that sum fraction INTO the fraction of Dems who oppose the legislation.

I'm afraid I made the problem harder than it needs to be by asking you to use my formula:

No. of likely Demo voters who opposed the legislation
-------------------------------------------------- = ???
Total number of people who opposed the legislation

Try again, using only the decimal fractions mentioned immediately above.

Answer 9

.1/.35=.2857?

Answer 10

@mathmale

Answer 11

that's the result I get. I believe we're correct.
See how simple the problem becomes, once we realize we can ignore the counts of Dems and Repubs, and that we need focus only on the "Oppose" line of this table?

Answer 12

I hope so, I never know with this teacher! Thank you for your help!