Question

Five marbles are randomly selected with replacement. The probability of a black marble being chosen is 15%. What is the probability that at least 2 marbles are black?

Answer 1

Let X be the number of black marbles drawn, then X ~ Bin(5,0.15). Now calculate P(X>=2).

Answer 2

(x>=2) or (x=2) ?

Answer 3

Well, it's more convenient to calculate the complement probability first, that is P(X<=1)

Answer 4

so, if I find the compliment, it would be (5c1) * (.15)^1 * (.85)^4 + (5c2) * (.15)^2 * (.85)^3

? ? ?

Answer 5

No, P(X<=1) = P(X=0) + P(X=1)

Answer 6

You should read '<=' as 'less than or equal to'

Answer 7

Right.

Answer 8

"No, P(X<=1) = P(X=0) + P(X=1)"

I don't have any idea where to go from here.

Answer 9

Calculate P(X=0), and then P(X=1) , and then add them up to find the complement probability.

Answer 10

hmm

Answer 11

Well, you know the formula right? P(X=k) = nCk*p^k*(1-p)^(n-k), just plug the numbers in

Answer 12

yeah, just having a hard time attributing the variables. Would "n" be 5?

Answer 13

Aw well... - Don't feel obliged to continue to put up with me any longer. I'll stay with my professor tomorrow. Thank you for your patience and help.