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# S1 probability distribution help please! watch

1. Repeated independent trials of a certain experiment are carried out. On each trial the probability of success is 0.12

(i) Find the smallest value of n such that the probability of at least one success in n trials is more than 0.95

N = 24 is the answer

I don't understand how to work it out. (It's from OCR June 2009, just if you're wondering).

2. (Original post by Jasminea)
Repeated independent trials of a certain experiment are carried out. On each trial the probability of success is 0.12

(i) Find the smallest value of n such that the probability of at least one success in n trials is more than 0.95

N = 24 is the answer

I don't understand how to work it out. (It's from OCR June 2009, just if you're wondering).

Think of it this way, in n trials,what is the probably of having 0 successes?
3. (Original post by SeanFM)
Think of it this way, in n trials,what is the probably of having 0 successes?
Well, I thought you could say 1 - P(X=0) > 0.95 or something like that but I'm confused with what P(X=0) because I would assume it's 0.88 as it fails on the first go or do you use the geometric distribution equation?

But then there's no n included and if you use the equation, I thought you'd say 0.12(1 - 0.12)^n-1
4. (Original post by Jasminea)
Well, I thought you could say 1 - P(X=0) > 0.95 or something like that but I'm confused with what P(X=0) because I would assume it's 0.88 as it fails on the first go or do you use the geometric distribution equation?
Geometric distribution doesn't need to come into it, remember that one or more successes in n trials is the complement of no successes in n trials.

And yes you are correct, P(X=0) is 0.88.. so you just need to use this in your question
5. (Original post by SeanFM)
Geometric distribution doesn't need to come into it, remember that one or more successes in n trials is the complement of no successes in n trials.

And yes you are correct, P(X=0) is 0.88.. so you just need to use this in your question
Sorry but what do you mean by the complement. I know you have to solve an equation but what? I don't understand
6. Actually, don't worry, I get it now.

Thanks for the help
7. (Original post by Jasminea)
Sorry but what do you mean by the complement. I know you have to solve an equation but what? I don't understand

Sorry, I think complement is the wrong word to use.. but the word escapes me.

For example, if I had a rock paper scissors game where the probabliity of winning, losing or derawing was each 1/3... and I asked you what's the probability of you either losing or drawing 8 games out of 10... the (insert word here) other way of calculating it is finding the probability of winning 2 games out of 10, if that makes sense.. and you can apply something similar here (but using 1 - .... ) to find the probability requested.

Or another example, probability of flipping 5 heads out of 6 is the same as flipping 1 tails out of 6.
8. (Original post by Jasminea)
Well, I thought you could say 1 - P(X=0) > 0.95 or something like that
Very good!

If you then take 1 from both sides you'll end up with an identity. You'll want to get rid of - P(x = 0) and you can do that by multiplying by -1, recalling what happens to the < or > sign in an equality when you do so.

To make further progress, what kind of distribution are we working with here? If you try the most obvious one, you should be able to set up an equation that is solveable. HINT we have a fixed number of trials (that's n) and a constant probability of success. What dstribution fits these criteria?

PS you are also right that p = 0.88 comes into it.

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