## Betcha Find a Chocolate

Laura saw that there were three pieces of candy left in a bowl on the kitchen table. She knew they were either chocolates or caramels but didn’t know how many there were of each. What is the probability that there is a piece of chocolate candy in the bowl?

7/8.

The possible combinations are:

1. Chocolate Chocolate Chocolate

2. Caramel Caramel Caramel

3. Chocolate Chocolate Caramel

4. Caramel Caramel Chocolate

5. Chocolate Caramel Caramel

6. Caramel Chocolate Chocolate

7. Chocolate Caramel Chocolate

8. Caramel Chocolate Caramel

Number 2 is the only one that doesn’t have chocolate, thus Laura’s love of chocolate will more than likely be satiated.

3 Comments on "Betcha Find a Chocolate"Mark says

May 4, 2019 @ 09:26

This answer is not correct. You’ve double counted possible combinations. For instance: Caramel Caramel Chocolate and Chocolate Caramel Caramel are the same combination, just different order which does not matter in this problem. There are really only 4 combinations with only 1 not having chocolate. Therefore the answer is 75%.

Dan says

May 4, 2019 @ 11:11

The order does matter because you have to account for all possible outcomes. The two you described are both separate, possible outcomes.

AlchemiCailleach says

June 10, 2019 @ 20:57

She does not know how many of each were in the bowl, but given that the candies were either chocolates or caramels, we will assume for now at least, that the likelihood for each candy is 50%.

There IS an error in the combinations for the answer.

Using binary, we can see what all the combinations are supposed to be.

Notably, across 8 possible combinations (drawing 24 total candies), there end up being 12 chocolate and 12 caramels still – consistent with the 50% probability of each candy being either chocolate or caramel.

1: 000 c – c – c 0 choc

2: 001 c – c – ch 1 choc

3: 010 c – ch – c 1 choc

4: 011 c – ch – ch 2 choc

5: 100 ch – c – c 1 choc

6: 101 ch – c – ch 2 choc

7: 110 ch – ch – c 2 choc

8: 111 ch – ch – ch 3 choc

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