Suppose I have 100 balls in a box and 10 of them are red. If I randomly take out 40 of them, what is the probability that I can get at least 6 red balls? How is this worked out?

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!

## All Answers (5)

Audil Khaki· American University of Middle East, KuwaitYou may use Excel Formula for this and work it out as:

=HYPGEOMDIST(6,40,10,100)

Which works out to 10%

Kieran Mccaul· University of Western AustraliaPavan Jindam· Reserve Bank of IndiaJoykrishna Pramanik· Indian School of MinesWen Wang· University of Minnesota Twin CitiesCan you help by adding an answer?