Need help with probability?

Question

You are walking along a path of length 7 (i dont know why but you are) each one of your paces i 1 long (it will take you 7 paces). However for each pace you have a 1/9 chance of slipping and dying a horrible death, how probable is it that you will die? I made up the numbers, its the understanding i need, but i dont really want a word answer is there an equation by any chance as i really need this method for a much more meaty example? P.s. im sure that the probability of you actually dying walking along paths will be greatly smaller than this examples answer (at least i hope so)

Answer 1

Probability is really tricky.
In this example, the probability of dying per step is 1/9, therefore the probability of surviving that step is 8/9.

If you take a journey of 2 steps, you are more likely to die, less likely to live, than in a 1-step journey.
The probability of surviving the 2-step journey is 8/9 x 8/9 = 64/81, so the probability of dying is 17/81. (0.20988)

3 steps : living 8/9 x 8/9 x 8/9 = 512/729, so dying=217/729 = 0.29767 (getting worse)

so 7 steps : probability of living is (8/9)^7 = 0.43846
probability of dying is 0.56154, so by now you are more likely to die than live, but no matter how many steps you take, there's always a chance that you survive.

Answer 2

You need to set up a binomial where p is the probability of dying for each pace (1/9) and thus q is the probability of not dying (8/9). So, for 7 paces, we can write:

(p + q)^7 = (1/9 + 8/9)^7 and the terms of the expansion will give you the probability of definitely dying as 1/9 raised to the power of 7 and the probability of not dying as 8/9 raised to the power of 7.

However, there is some fallacy in the set up since the other terms really are not meaningful inlike tossing of a coin and getting heads and tails.

If we simply say that 7/9 is the probability of death in 7 paces, then we end up with another fallacy that in 9 steps, the death is certain.

I strongly suggest that you post the real problem.

Answer 3

You have to be really careful with probability.

There is a strong temptation here to do a cumulative probability - you treat each step as a separate event and therefore you simply sum the probability of dying on each step (1/9 * 7) = 7/9.

However this is the incorrect approach, because this is only valid if the probability of each event is genuinely unrelated to the previous events. In this case it's actually NOT unrelated - clearly if you die on the first step your probability of dying on the second one is actually zero, because you can only die once!

The correct approach is therefore to calculate the probability of NOT dying, and then invert it. The probability of not dying is
(8/9)^7 = 0.4385. The probability of dying is therefore 1-0.4385 = 0.5615

As a formula, let Ps be the probability of slipping, Pd be the probability of dying, and Ns be the number of steps.

Pd = 1-(1-Ps)^Ns

Answer 4

The answer is 1/9 * 7 = 7/9. The previous answer, with 1/9^7 power is quite improbable considering the fact that the chances of dying are much greater than : 1/4782969.

Answer 5

well...
add the chances of dying at each step up to get the overall probability of dying. in this case we have a geometric progression whereby X~Geo (1/9) where X is the step number and 1/9 is the probability of dying.it is not a binomial distribution as once you die, you stop taking more steps, hence it has to be geometric i.e. you continue until success. i assume each step is independant of any previous steps.
in a geometric distribution... P(X=x)= p(1-p)^(x-1) where p is the probability of success.
so now we need to work out P(X=1)+P(X=2)+...+P(X=7) as you could die on any one of those steps. anything after P(X=7) is omitted as the path has ended and you survive...
now summing those probabilities gives...
0.56154 (5dp) (as said by Nick J earlier)
another method would be to use a tree diagram where by each route to death is explored and once death occurs, the branch of the tree is truncated, and then sum the probabilities of these deaths. this will give you the same answer.
remember on a tree diagram... multiple probabilities as you go along the branches and add them if you look at different branches.

Answer 6

I'd say P(live) = 8^7 / 9^7 = 2097152 / 4782969

Therefore, P(Death) = 1 - (8/9)^7
= 1 - 2097152 / 4782969
= 2685817 / 4782969
~ 0.56

So there's just over a half chance that you will die walking down this treacherous path

Answer 7

hmmm i would say it is...

1/9 x 1/9 x 1/9 x 1/9 x 1/9 x 1/9 x 1/9 =

or 1/9 to power of 7 can't do a 7 like that on here sorry

Answer 8

1/9^7 would be the probability of dying on the 7th step as opposed to dying at any other point

Answer 9

by using d tree diagram, u wil notice dat

P(die)
=7(1/9)
=7/9

note:im NOT 100% sure dis is correct.

Answer 10

d