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Meg
06-18-2011, 03:26 AM
It's late, I'm exhausted and for some reason this question is not working for me.

A sample of 400 people were given a taste of two products (A and B). Assuming no preference for the products, what is the probability that 210 or more pick brand A?

What would you say? Or how would you solve it? :o

I could re-read the chapter, but my brain hurts.

CarterandSawyersMom
06-18-2011, 03:42 AM
I wish I could help! I am not a math person. Hubby just went upstairs to check on Maguire I am sure he would have the answer.. i will check back in when he comes down.

Meghan
06-18-2011, 04:35 AM
When i read the subject line I figured I'd be able to help but then saw it was probability so I suck lol

Good luck

teacher_mom
08-30-2011, 02:14 PM
Sorry it is a little late, but maybe I can help. Note that I can't format things very well, so you may have to excuse my use of words in place of proper mathematical formulae.

Assuming there is no preference then the probability of A P(A)=0.5 and P(B) = 0.5
If we define a "success" as choosing product A, then a failure is a person choosing product B.
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The probability of getting exactly 210 successes is computed as follows.
Then we apply the binomial distribution for P(210|400) (the probability of 210 successes out of 400 trials.
P(210|400) = [400 choose 210] (0.5)^210(0.5)^190
Which simplifies to
P(p=210) = (400 choose 210) 0.5 ^400
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To determine the probability of AT LEAST 210 successes you must take the sum from n=210 to n=400
P(p>=210)= Sum (n=210 to 400) (400 choose n) (0.5)^n(0.5)^(400-n)
This simplifies to
P(p>=210)=0.5^400 [Sum (n=210 to 400) (400 choose n)]

At this point, I would realize that I have forgotten all the identities using binomial coefficients and I would write a quick program to attempt to do the math for me.

Or I would reread the chapter and look for a darned shortcut.

Gosh do I hate probability. It is probably the only course I hope to never teach, but evaluating a problem this complicated is fortunately beyond the level of high school math.

Even if this was way too late, I thank you for providing me with a stimulating problem to keep me from going to mush during my mat leave.