Probability: There are 10 chocolates or identical appearance. 3 are caramel and 7 are mint. Hugo randomly selects and eats 3 chocolates.?

(a)
Suppose hugo eats X caramel chocolate.
Then X ~ hypergeometric distribution.

P(x)
= C(3,x) * C(7,3-x) / C(10,3)
=C(3,x) * C(7,3-x) / 120

P(1)
= C(3,1) * C(7,2) / 120
= 3 * 21 / 120
= 0.525 ..... Ans

(b)
P( X ≧ 2 )
= P(2) + P(3)
= [ C(3,2)*C(7,1) + C(3,3)*C(7,0) ] / 120
= ( 3*7 + 1*1 ) / 120
= 22 / 120
≒ 0.183 ..... Ans