Question 257524
An urn contains 10 red balls and 5 blue balls. Five balls are chosen at random with replacement from this urn. 
(a) What is the probability that all five balls drawn are red?
n = 5 ; p = 2/3 ; x = 5
P(5 red) = (2/3)^5 = 0.1317
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(b) What is the probability that among those five there are at least one red ball and also at least one blue ball?
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P(no red in 5) = (1/3)^5
P(no blue in 5) = (2/3)^5
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P(at least one red and one blue) = 1 - [(1/3)^5 + (2/3)^5]
= 0.86419..
Cheers,
Stan H.