Any probability experts here? This is pretty fuckin amazing. :P
 

I just read a BBC article, about a woman who failed to pass the written portion of her driving license test.

949 times.

So that made me think about the odds of that actually happening. It's a multiple choice test, and you need to get 60% to pass, according to the article.

I don't think it's possible to do an exact math equation without knowing how many choices there were for each question... However a rough guess might be possible by someone good at probability math..

I think it would be AMAZINGLY hard to fail any test like this 950 times. I mean I think I could pass any multiple choice test, with 50 questions, only needing 60% to pass, with 950 attempts? in ANY language?

Did she just pull off an Indiana Jones?

http://news.bbc.co.uk/2/hi/asia-pacific/8347164.stm

Frankly I'm glad she doesn't have a license. Anyone that stupid certainly shouldn't be on the road. LOL

it's easier to sign up a porn site

Suppose each question has the same number of choices, n. Let m be the number of questions.

So there are n^m possible test answer configurations which can be submitted with only 1 being 100% correct. The probability of choosing the right answer on any one question at random is 1/n. So, the probability of choosing x% correct answers at random is (100/x) * n^(-m).

So even with n=4 and m=20, the probability of guessing and getting 60% is 5/(3*4^20) which is a microscopic percentage.

This is assuming they are being chosen completely at random, though.

I'm more of a dumbass than I thought.


.

As a followup, this would be equivalent to someone giving you an alphabet with n characters and then they say, hey I am going to construct a word out of those characters with length m. Think about how long it would take you to get > 60% of the characters in the right spots.

Say the alphabet was {a,b,c,d} and they are going to construct a 20 letter word using just those characters. It'd be pretty difficult to get 60% correct at random.
Iteratively, you'd have:
aaaaaaaaaaaaaaaaaaaa
baaaaaaaaaaaaaaaaaaa
caaaaaaaaaaaaaaaaaaa
daaaaaaaaaaaaaaaaaaa
abaaaaaaaaaaaaaaaaaa
acaaaaaaaaaaaaaaaaaa
.....
dddddddddddddddddddd

A shitload! ;)

I can't do that kind of math, I failed Algebra 5 times...

But at least I was smart enough to know when to quit!

// 50 questions
// 4 random answers

// 60%+ correct = pass
// 30 questions correctly out of 30 = 60%

$questions = _createTest(50,4);
$answers = _answerQuestions(50,4);
$correct_score = _correctTest($questions, $answers);
$passed = 0;


$count = 1;
while ($passed <= 1) {
echo "Taking test #" . $count. "\n";

$questions = _createTest(50,4);
$answers = _answerQuestions(50,4);
$correct_score = _correctTest($questions, $answers);

echo "You're correct answers on test #" . $count . "was " . $correct_score . ".\n";
if ($correct_score >= 30) {
"You Passed the test on the $count try"; exit;
} else {
"You failed\n Retaking test again..."; $count = $count + 1;
}
$count = $count + 1;
}
exit;

function _createTest($questions, $choices) {

$question_array = array();
for ($i=1; $i<=$questions; $i++) {
$question_array[] = rand(1,$choices);
}

return $question_array;

}

function _answerQuestions($answers, $choices) {

$answer_array = array();
for ($i=1; $i<=$answers; $i++) {
$answer_array[] = rand(1,$choices);
}

return $answer_array;
exit;
}

function _correctTest($questions, $answers) {

$theanswers = $answers;
$i = 0;
$correct = 0;
foreach ($questions as $solution) {
//echo "Correct Answer: $solution | Your Answer: $theanswers[$i]\n";
if ($solution == $answers[$i]) { $correct = $correct + 1; }
$i = $i + 1;
}

return $correct;

}

i passed it on the first run in 877,000 test tries 8:01
2nd run as at 2 million mart and still not passed 8:01
out of 15 questions, if you random pick you average about 15 correct and need 30 correct to score %60


yeah, I didn't write this!!

almost forgot... odds to pass test entering random numbers is problably 1 in 4 million

Did she pass?

I'd say the probability of her having an accident before long is higher.

Sounds like she'd even be prone to having an accident in a parked car. At least when Edison failed 1000 times or however much it was, he was trying to invent the light bulb. All she's going to get when she passes that test is the ability to legally crash a car.

must have memory like a goldfish, because the questions have to be substantially the same every time, right?