# Simple Probability question

1. Apr 19, 2011

### the riddick25

1. The problem statement, all variables and given/known data
There is a drunk man who is just leaving the pub, he is so drunk that the probability of him taking a step forward is 0.5, and the probability of him taking a step backwards is also 0.5
There is a zero chance of him not taking a step.
After 20 steps, what is the probability of him being 14 steps back into the pub?

2. Relevant equations
Not sure

3. The attempt at a solution

I have no idea where to start for this question, so if somebody could give me a push in the right direction that would be extremely helpful

2. Apr 19, 2011

### GatorPower

How many ways can 14 steps backwards be done? How many outcomes are there in total?

3. Apr 19, 2011

### eczeno

we can put the question in more familiar terms. say you flip a coin 20 times. what is the probability that you flipped 14 more heads (back steps) than tails (forward steps)? So, as gatorpower said, it is just a matter of counting how many ways that can be done.

good luck

4. Apr 19, 2011

### HallsofIvy

Staff Emeritus
This is a binomial distribution with p= q= 1/2 and so will involve $(1/2)^{20}$.
Let n be the number of forward steps he took. Then 20- n is the number of backward steps. Assuming he started at the door, if he is 14 steps back into the pub, taking forward steps positive and backward steps negative, we must have n- (20- n)= 2n- 20= -14. Solve that for n.

Now that you know the number of forward and backward steps, you can use the binomial coefficient to determine in how many orders he could have taken those forward and backward steps.

(By the way, I find this problem, and any problem postulating people not in control of themselves, offensive.)

5. Apr 19, 2011

### eczeno

I agree with halls, why do we need such unpleasant topics for math problems?

6. Apr 19, 2011

### the riddick25

Thank you all very much for your help

and i agree with what you said about the question, like eczeno said this could easily have been put in terms of a coin flipping, instead it is about a drunk person who cant walk properly :S