A jar contains five black buttons and six brown buttons. If eight buttons are picked at random what is the probability that at least four of them are black

Question

Need percentage,I could not get the answer to the question, nor know how to do it. I am not good at this type of math. And I am not good at word problems either. Need help please.

Answer 1

x=5

y=6

x+y=11

P(x) = 5/11

P(y) = 6/11

P(x>3) = 11C4(5/11)^4(6/11)^7

+ 11C5(5/11)^5(6/11)^6

+ 11C6(5/11)^6(6/11)^5

+ 11C7(5/11)^7(6/11)^4

+ 11C8(5/11)^8(6/11)^3

+ 11C9(5/11)^9(6/11)^2

+ 11C10(5/11)^10(6/11)^1

+ 11C11(5/11)^11(6/11)^0

or P(x>3) = 1-P(x<4)

= 1- 11C0(5/11)^0(6/11)^11

-11C1(5/11)^1(6/11)^10

-11C2(5/11)^2(6/11)^9

-11C3(5/11)^3(6/11)^8

which is still tedious, but a few less calculations needed

nCr = n!/r!(n-r)!