12 in a row wrong in multiple choice, what are the odds

I checked SFSC's math and agree that it's 3% assuming four choices per question.

Why would your daughter "throw" her PSAT's - this is not even a test that means anything....

No idea the real reason here but one reason I can think of is to lower expectations. If a kid performs poorly on a PSAT, their parents are likely to be pleased with a not so great but slightly higher score on a test that means something. If a kid tests and gets D's constantly and then pulls a C+ at the end, there is going to be a small amount of celebration, even though a C+ is nothing to get excited about under normal circumstances. 

Just a theory, doesn't necessarily apply to the OP and his kid. 

If she didn't throw the test on purpose then she needs to go buy a lotto ticket today! 3% is pretty durn good! Maybe even ask her for some picks on this weekends games OP.

She doesn't want to be seen as smart.  Too much like her big sister who is not as smart but way more academically driven.

It kills me that she is not achieving her potential.  But I was a National Merit scholar with a B Average.  So Karma!

She'll likely outgrow it.....I'd leave it alone.  If she's smart she'll figure it out.

I could be wrong (no personal experience).  I don't think that kids are that sophisticated.  If she wanted to throw it to prove a point - she would get all of them wrong.  Why pick the last 12?

The decision making to throw JUST the last 12, while working hard on all the rest, just to prove some point seems to vague and obscure and complicated of a thought process just to make a simple point of "I'm not smart" when getting ALL of the wrong would do that better.  I'm not sure kids or as capable at "subtle" messages that would take you effort to decipher.

When I see kids say they can't do something and try to prove it?  They look comical in their over exaggeration in their inability to make SURE you know they can't do it.

3% is right...well...3.16%.  (0.75^12).  If there were 3 choices then it would be a 0.7% chance.  5 choices would be 6.9%.

At first I thought that maybe she skipped a question without knowing and messed up the coordination between which number she was looking at in the question booklet and which number she was filling in on the answer sheet.  But the probability should still be the same assuming the test isn't programmed to have succeeding questions have the same choice answer two times in a row.  Which would be kind of silly.

I wonder how hard it would be for me to take something like the SAT and purposely get everything wrong.  Obviously if I'm smart enough to know all the answers, I can do it...but since I don't know all the answers, I'd eventually have to guess which is the wrong answer on a bunch of questions.  Sometimes there is usually one choice that is obviously wrong...so that helps...but I just wonder if I could do it.  Odds say I probably can't though...so maybe that will motivate me more?  

This stands out to me.
If she is seeing/observing big sister struggle with being/becoming "smart" it's not a giant leap for little sister to say "looks like too much work, I'll pass" and this is an easy way to get out of it. 

Armchair psychology, I know.

But I had these thoughts in hindsight when I realized how hard advanced math was after geometry. I wished SO HARD that I would have played dumb in middle school so I would have never been identified as "advanced." I would have easily gotten a 4.0 if it weren't for trig and calc (which the "regular" kids don't have to take). TO THIS DAY: GRRRRR.

maybe she got to the end of a REALLY LONG test, that means absolutely nothing and realized that she really JDGAF.

Here is an interesting article I read not long ago about how children respond to praise. A quote from the article " Giving kids the label of “smart” does not prevent them from underperforming. It might actually be causing it."

I would also recommend reading the book Mindset: The New Psychology of Success written by Carol Dweck. It was recommended to me in a BT thread last Fall and it really made an impact on how I work with my kids and what I say to them about their achievements.

http://nymag.com/news/features/27840/

If there are four choices for each question then the probably  of getting some of the twelve questions right by guessing is 25%.   To get all of them wrong by guessing has a change of 3.16% as stated above.   To purposely get all of them wrong requires the test taker to know all the right answers and then choosing the wrong answer.   

Either way, you have one smart daughter.

+1

agree with this theory as well - there have absolutely been times when i sat through pointless tests - or tests i already knew i passed - and answered a series of C's to get out faster.  and a PSAT?  i never even took that - that is a waste of time/money test especially if your kid IS smart.  it's a great tool for bad test takers to practice for the real one, but a huge waste for a smart kid.

^^ I think the best guess will be based on what she told the OP about it.

Getting off by one row on a handwritten test can really mess you up, too.