Anyone remember any a-level stats?

[Guest Kether]

You have a 35 question multiple choice test, each question has four answers. The pass mark is 30 out of 35.

 

What's the probability of passing if you answer all the questions at random?

 

Had a go at this using logic and was sure I was right but then got all confused and I can't remember how we did it at school.

 

Hmph.

[LiquidEyes]

It's a binomial distribution.

 

p=1/4 (the probability of success per trial)

q=3/4 (prob. of failure)

n=35 (number of trials)

 

Can't for the life of me remember the formula though...

[LiquidEyes]

QUOTE (Kether @ Apr 16 2004, 11:01)

What's the probability of passing if you answer all the questions at random?

BTW - intuitively, the answer is "piss poor".

[Tresh]

You have an 1/4 chance of getting each right and you need to get 30 right.

 

Simply 1/4 muliplied by itself 30 times. Thus the chances of getting it right will be 1/1152921504606846976.

 

Not a lot in other words.

[Tresh]

Scrap that, it's wrong, forgot u've got 35 chances.

 

It is a bionomial distribution as said above. Still it equates to "pigs might fly"

[LiquidEyes]

Trust me it's not that simple Tresh.

 

The flaw in your reasoning, is that there are many different permutations of right & wrong answers that will still lead to 30 or more correct answers. Hence the formula contains assorted exponential and factorial functions!

[Tresh]

As recognised in the post above.

 

It is about 5 years ago I sat Stats for my A-level maths, got an A as well. That is memory loss for ya.

[LiquidEyes]

Just had a quick swot-up online...

 

Okay the probability of getting 30 correct answers (exactly 30) is

P(X=30) = C(35,30) * (p^30) * (q^(35-30))

= 324632 * 8.673e-19 * 0.237

= 6.681e-14 (very very very small!!!)

 

The probability of passing the exam is P(X>=30)

= P(X=30) + P(X=31) + ... + P(X=35)

 

So by my calculations:

 

P(X=30) = 324632 * 2.058e-19 = 6.681e-14

P(X=31) = 52360 * 6.860e-20 = 3.592e-15

P(X=32) = 6545 * 2.286e-20 = 1.496e-16

P(X=33) = 595 * ...

P(X=34) = 35 * ... (can't be arsed working out the rest)

P(X=35) = 1 * ...

 

The total going to be just over 7e-14 (0.00000000000007)

 

So you have a probability of about 1 in 14,000,000,000,000 of passing the exam!

[LiquidEyes]

QUOTE (Tresh @ Apr 16 2004, 11:41)

It is about 5 years ago I sat Stats for my A-level maths, got an A as well.

Ditto ... been about 8 years! At least some of my brain cells have survived.

[Guest Kether]

QUOTE (LiquidEyes @ Apr 16 2004, 12:04)

Just had a quick swot-up online... Okay the probability of getting 30 correct answers (exactly 30) is P(X=30) = C(35,30) * (p^30) * (q^(35-30)) = 324632 * 8.673e-19 * 0.237 = 6.681e-14 (very very very small!!!) The probability of passing the exam is P(X>=30) = P(X=30) + P(X=31) + ... + P(X=35) So by my calculations: P(X=30) = 324632 * 2.058e-19 = 6.681e-14 P(X=31) = 52360 * 6.860e-20 = 3.592e-15 P(X=32) = 6545 * 2.286e-20 = 1.496e-16 P(X=33) = 595 * ... P(X=34) = 35 * ... (can't be arsed working out the rest) P(X=35) = 1 * ... The total going to be just over 7e-14 (0.00000000000007) So you have a probability of about 1 in 14,000,000,000,000 of passing the exam!

That's what I did I think but couldn't remember the formula for the binomial thingy.

 

I did P(30, 31... 35)

 

so that gives you... 0.25^30 + 0.25^31...+ 0.25^35.

 

Some twat on gurn seemed to think the answer was 1/120.

[LiquidEyes]

QUOTE (Kether @ Apr 16 2004, 12:33)

Some twat on gurn seemed to think the answer was 1/120.

LOL

 

Answering completely randomly, the odds are that you'll get a score of 3 to 15 (over a 99% probability).

 

There's a 99.999% chance you'll get 20 or less and the distribution tails off even more rapidly above that!

Edited April 16, 2004 by LiquidEyes

[Guest Kether]

QUOTE (LiquidEyes @ Apr 16 2004, 12:39)

QUOTE (Kether @ Apr 16 2004, 12:33) Some twat on gurn seemed to think the answer was 1/120.  LOL   Answering completely randomly, the odds are that you'll get a score of 3 to 15 (over a 99% probability).   There's a 99.999% chance you'll get 20 or less and the distribution tails off even more rapidly above that! I sent a PM to the person who posed the question saying not to believe that answer but I didn't have the confidence to back it up.   I'm glad my intuition was correct, I had a little standard deviation graph in my head and thought 1/120, no way!

[LiquidEyes]

Check out this site.

[LiquidEyes]

^ the probability distribution for your hypothetical multiple choice exam.

[Tresh]

Most people will look at this and think how sad...

 

I found it genuinely interesting tho.