The first problem deals with criminal convictions:(adsbygoogle = window.adsbygoogle || []).push({});

It takes 9 out of 12 jury members to convict a defendent. 65% of all defendents are guilty. Jury members make their decisions independent of each other. Probability that a juror votes a guilty person, innocent is .2 whereas the probability that a juror votes an innocent person guilty is .1

Find the probability that the jury renders a correct decision.

- Now i see this problem as a problem with two cases:

(1) when the jury votes an innocent person, not guilty

(2) and when the jury votes a guilty person, guilty.

leading to two seperate probability, and i believe the two cases are mutually exclusive.

also, i let X be a random variable with binomial distribution where X is the number of jurors who vote an innocent person not guilty.

^ i believe that is case 1

and i let Y be a similar random variable as X, where X is the number of jurors who vote a guilty person guilty.

but my gut feeling makes me believe that this does not work.

any helpful hints from you guys?

and here is the other problem:

a certain typing agency employs 2 typists. one typists averages 3 errors per article and another averages 4.2 errors per article. the probability of using either typist is equal. what is the approximate probability that my article will have no errors?

i know it deals with expected values and the Poisson distribution, but i dont know how to setup the E(g(X))

ie, I let X be a random variable with Poisson distribution where X is the number of errors per article, and i find the values for each typist when X is 0.

do i just take their respective probabilities of them making zero errors, say A and B, and then setting up E(X) = .5A + .5B?????

thanks guys, ive just been really unsure about myself lately and i lost a lot of my confidence

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# Homework Help: Some probability questions that are bugging me

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