SOLUTION: You have a box of chocolates that contains 20 pieces of which: 5 are solid chocolate, 8 are filled with cashews, and 7 are filled with cherries. All the candies look exactly al

Algebra ->  Probability-and-statistics -> SOLUTION: You have a box of chocolates that contains 20 pieces of which: 5 are solid chocolate, 8 are filled with cashews, and 7 are filled with cherries. All the candies look exactly al      Log On


   

Question 1159688: You have a box of chocolates that contains 20 pieces of which:
5 are solid chocolate,
8 are filled with cashews, and
7 are filled with cherries.
All the candies look exactly alike. You select a piece, eat it, select a second piece, eat it, and finally eat one last piece.
(a) Find the probability of selecting a solid chocolate piece followed by two cherry-filled chocolates.

(b) Find the probability of selecting a solid chocolate piece and two cherry-filled chocolates in any order.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

(a)  P = %285%2F20%29%2A%287%2F19%29%2A%286%2F18%29 = %281%2F4%29%2A%287%2F19%29%2A%281%2F3%29 = 7%2F228 = 0.030702.     ANSWER



(b)  I interpret these words "in any order", as if they relate to each such a triple.


     P = %28C%5B5%5D%5E1%2AC%5B7%5D%5E2%29%2FC%5B20%5D%5E3 = 


               Next,  C%5B5%5D%5E1 = 5;   C%5B7%5D%5E2 = %287%2A6%29%2F2 = 7*3 = 21;   C%5B20%5D%5E3 = %2820%2A19%2A18%29%2F3 = 20*19*6 = 2280.


       = (therefore, I continue) = %285%2A21%29%2F2280 = 21%2F456 = 7%2F152 = 0.0460.      ANSWER

Solved.