SOLUTION: Been out of school a while and I'm required to take an SPC course for work and having difficulty understanding how an answer was calculated. Urn contains 1000 Black Beads, 4000

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Question 648329: Been out of school a while and I'm required to take an SPC course for work and having difficulty understanding how an answer was calculated.
Urn contains 1000 Black Beads, 4000 white beads, the example states the probability of getting exactly Five black beads in a random sample of 50 beads is 0.030 (3%), they don't show how this is calculated, was wondering if you could help.
Thanks.
Greg

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi,
Urn contains 1000 Black Beads, 4000 white beads, P%28Black%29+=+1000%2F5000+=+1%2F5+=+.2
Bionomial Distribution Probability
P(5B in sample of 50) = 50C5(.2)^2(.8)^45 = .03
Note: The probability of x successes in n trials is:
P = nCx* p%5Ex%2Aq%5E%28n-x%29 where p and q are the probabilities of success and failure respectively.
In this case p = .2 & q = .8 n = 50
nCx = n%21%2F%28x%21%28n-x%29%21%29