Statistics question on probability?

Question

Of those who voted in the 2000 and 2004 U.S. Presidential elections,
about 48% voted Republican in 2000
and about 51% voted Republican in 2004.

True or false: Since 0.48 x 0.51 = 0.24, about 24% voted for the Republican (George W. Bush) in both elections.
If true, explain why. If false, explain the flaw in logic.

Answer 1

False.

You don't know to what degree the Bush subset in 2000 overlaps with the Bush subset in 2004. Theoretically, it is possible that no one voted for Bush in both elections: the 48% who voted for him in 2000 may have chosen to vote for his opponent in 2004.

On the other hand, the number who voted for him in both elections could theoretically been 48%, if everyone who voted for him in 2000 also voted for him in 2004.

Practically, the answer is much closer to 48% than to 0%. I would say that it is probably around 42-43%.

Answer 2

The flaw in the calculation is in the multiplication of 48% and 51%.

You can only multiply probabilities in this manner when the two events are independant - they have no effect on each other.

In fact, many (or most) of those voting Republican in one election voted Republican in the other election. This is a "high correlation".

Answer 3

24% didnt vote for republic. if it did that wudnt make sense, because that is almost half of 51%. and thats more than half. 51% and 48%. so that means democrats had 49% and 52%. the democrats had about 51% of the election, and rebublicans had 49% (this isnt including the other parties no1 cares about)

Answer 4

I don't think that you could just multiply them and say that they voted in both election. I mean if you think about it 0 percent to about 48% of the people could have voted republican in both elections. I don't think that this makes sense.

Answer 5

your multiplying two unrelated sets giving a undefined variable