The Cookie Monster has a cookie jar. In this cookie jar, there are five chocolate chip cookies, six almond cookies and four raisin cookies. He places his hand into the jar and grabs 4 cookies without replacement.
a) What is the probability that he will get exactly 2 chocolate chip cookies?
b) What is the probability that he will get at least 2 chocolate chip cookies?
Prob(choc) = 5/15 = 1/3
prob(not choc) = 2/3
a) prob(exactly 2 chocs out of 4) = C(4,2) (1/3)^2 (2/3)^2
= 6(1/9)(4/9) = 24/81 = 8/27
b) at least 2 chocs ---> 2, 3, or 4 chocs
or NOT 0 or 1 choc
Prob(no choc) = C(4,0)(1/3)^0 (2/3)^4 = 1(1)(16/81) = 16/81
prob(1 choc) = C(4,1)(1/3)(2/3)^3 = 4(1/3)(8/27) = 32/81
prob(your event) = 1 - 16/81 - 32/81 = 11/27