An urn contains 5 red balls and 10 white balls. 6 balls are randomly drawn and not replaced. What is the probability that 3 or fewer balls drawn are red?

Answer 1

could be 3 red, 3 white
could be 2 red, 4 white
could be 1 red, 5 white
could be all white

prob of those taken in order from top to bottom
= C(6,3) (5/15)(4/14)(3/13)(10/12)(9/11)(8/10)
+ C(6,2) (5/15)(4/14)(10/13)(9/12)(8/11)(7/10)
+ C(6,1) (5/15)(10/14)(9/13)(8/12)(7/11)(6/10)
+ C(6,0) (10/15)(9/14)(8/13)(7/12)(6/11)(5/10)

= .... you do the button pushing

Can you see the pattern ?

Answer 2

The answer is supposed to be 0.04 + 0.25 + 0.42 + 0.24 = 0.95

However, when I do the math above, I get 0.01 + 0.03 + 0.04 + 0.04 = 0.12.

Where am I making the error in calculating this?