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August 17th, 2012, 11:51 AM   #1
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Independent trials of a random experiment

Let p(k) denote the probability of exactly k successes in n independent trials of a random experiment in each of which the probability of a success is p.
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[attachment=0:311jkpf6]#13.JPG[/attachment:311jkpf6]
where q=1-p.
Hence find the most probable number of successes when n=16 and p=0.2


I get that I must use Binomial distribution, but then what next? Please help..
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August 18th, 2012, 05:35 AM   #2
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Re: Independent trials of a random experiment

Hey UnscaryMidnight.

How many combinations of ways can you get k-successes in n independent trials? What about in k+1 trials? What's the ratio of the two (remember you have two probability statements: one concerning getting k+1 successes and another getting k-successes both for n trials)?
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August 19th, 2012, 09:49 AM   #3
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Re: Independent trials of a random experiment

sorry, im still struggling here. Could you do an example please?
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August 19th, 2012, 05:38 PM   #4
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Re: Independent trials of a random experiment

p(k) and p(k+1) are probabilities for getting k and k+1 successes from n trials. You know the PDF of a binomial so try calculating the ratio of these two expressions.
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