SOLUTION: there are 37 chocolates in a box,all identically shaped. There are 9 filled with nuts, 13 filled with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, an

Algebra ->  Probability-and-statistics -> SOLUTION: there are 37 chocolates in a box,all identically shaped. There are 9 filled with nuts, 13 filled with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, an      Log On


   

Question 1137421: there are 37 chocolates in a box,all identically shaped. There are 9 filled with nuts, 13 filled with caramel, and 15 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Two ways:

First way:

The probability of selecting the first piece as a solid chocolate is 15 out of 37, or 15/37.

Then 15/37ths of the time you select a solid chocolate and eat it.

Now there are only 36 pieces including only 14 solid chocolates.

So 14/36ths (which reduces to 7/18ths) of those 15/37ths of the time, you'll select a second solid chocolate.

So 7/18ths of 15/37ths is (7/18)(15/37) = 105/666 = 35/222ths, so the
probability is 35/222.

Second way:

(15 solids choose 2)/(37 pieces choose 2) = (15C2)/(37C2) = 105/666 = 35/222.

Edwin