SOLUTION: A bucket contains 6 orange balls and 8 yellow balls. 5 balls are to be selected at random. What is the probability that, of the 5 balls selected at least one is orange and at leas

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Question 229911: A bucket contains 6 orange balls and 8 yellow balls. 5 balls are to be selected at random. What is the probability that, of the 5 balls selected at least one is orange and at least one is yellow? What is the probability that, of the 5 balls selected at random, at least two are orange and at least two are yellow?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
8/14=fraction of yellow balls=y
6/14=fraction of orange balls=g
(y+g)^5=y^5+5y4g+10y^3g^2+10y^2g^3+5yg^4+g^5
a)
y^5=(8/14)^5=.0609 no orange
g^5=(6/14)^5=.0145 no yellow
1-(.0609+.0145)=.9246 probability of at least one ball of each color.
.
b)
10y^3g^2+10^2g^3
=10(8/14)^3(6/14)^2+10(8/14)^2(6/14)^3
=.5998 probability at least 2 balls of each color.
.
Ed