# Matching Socks

Pro Problems > Math > Statisics and Probabilities > Probability## Matching Socks

## Solution

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### A Box of Chocolates

Pierre assigns ratings to his chocolate candies based on how much he likes them, on a scale of one to ten, with one being the ones he likes the least, and ten being the ones he likes the most.

His box of chocolates has 20 candies, and he uses every integer value from one to ten in rating them. 5 of them are assigned the number 1, 4 are assigned the number 2, and 3 are assigned the number 3.

Pierre randomly chooses 3 chocolates, and he considers that he has an excellent snack if the combined total of the chocolate ratings is at least 25.

The probability that he will have an excellent snack isWhat is the total of the rating values for *all* the chocolates in his box?

### Thanksgiving Activities

Mr. Halliday is going to have 27 family members gathered together at his house on Thanksgiving. As each person enters the house, he provides them a ballot which they can use to vote for the activity they want to do on Thanksgiving. The ballot looks like this:

Watch a football game

Play charades

I don't care

Six people chose "watch a parade," eight people chose "watch a football game," four people chose "play charades," and seven people chose "I don't care."

The remaining people thought having a Thanksgiving Day ballot was ridiculous, and so they randomly checked an item without looking at it.

Mr. Halliday decided that if "I don't care" won the most votes, or if there was a tie between two choices, he would remove the "I don't care" ballots and then randomly select the activity by selecting one ballot from those remaining.

What is the probability that his guests will be watching football on Thanksgiving? Give your answer as a decimal rounded to four decimal places.

### Probable Digits

All the base ten digits from 0 to 9 are placed in a hat, and three are drawn at random, to form a three digit number. What is the probability that the resulting number is a multiple of 2, 5, and 9?

Note: the first digit is not a zero, since that would technically be a two digit number.