### Topics

- Use Hypergeometric Probability.

You may use Excel Formula for this and work it out as:

=HYPGEOMDIST(6,40,10,100)

Which works out to 10% - This is the probability of exactly 6 red balls. To find the probability of at least 6 red balls, you also need to calculate the probabilities of 7, 8, 9, and 10 balls as well and then sum them all. Using Stata, I make it to be 15.4%.
- I agree with Kieran Mccaul....if ur sampling scheme is without replacement then the distribution is Hypergeometric and if with replacement, it is binomial distribution....and the above probality is...P(X>=6)= 1-F(5)
- This is a Hypergeometric Distribution if you are drawing all the balls at a time. To compute this numerically we have: x={1-P(no. of red balls <=5)} . Now total no of ways to find such condition is:n=(90C40)+(10C1*90C39)+(10C2*90C38)+(10C3*90C37)+(10C4*90C36)+(10C5*90C35). Now from the classical definition P(no of red balls <=5)=n/(100C40)=0.846..So our required probability =1-0.846=0.154... I think you are with primary level probability problem, so i've an elaborated solution! hope it will help you!
- Thanks everyone for your inputs!

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