Adding and Subtracting Rational Expressions Question.

[babymathteacher]

Hi all,

I've been scratching my head at the question posted below. I have a feeling the answer key is incorrect. Could someone please verify.





Here is what the solutions say:




Best,
babymathteacher

 

[Dr.Peterson]

Hi all,

I've been scratching my head at the question posted below. I have a feeling the answer key is incorrect. Could someone please verify.


View attachment 35929


Here is what the solutions say:

View attachment 35930


Best,
babymathteacher

They clearly divided 24 by 3 and got 6 rather than 8, so they are wrong.

But since probabilities can't be greater than 1, clearly the problem is wrong when your answer is 4/3.

So probably the expression was supposed to have 18 instead of 24 in the numerator; making this change, you would have obtained the same results they show.

I haven't taken the time to do the probability work to derive their function, since that is obviously not something you are expected to do. One of us will, eventually!

 

[babymathteacher]

Thank you! That helps.

 

[Dr.Peterson]

Thank you! That helps.

I've looked into the formula they give, and I can see how they probably got their formula (with the 24) by overlooking one step -- I did the same at first. But I was right that it should be 18.

Their answers for 5 and 4 balls are clearly correct. (With 4 balls, you're certain to win, so 1 is right; with 5 balls, once you've seen that the first ball is yours, it's equally likely that the one ball they don't draw is one of your other two, or one of the two you didn't pick, so 1/2 is right.)

So I'd guess that they got 24 at first, realized the answers made no sense, and corrected it to 18 in their solution, but not in the problem itself. I've seen that sort of thing before.