The Wednesday Morning Math Challenge: Week 13

Welcome to Week 13 of the Wednesday Morning Math Challenge. You can find solutions to the week 12 puzzles here, along with — more importantly — discussions of some ways to approach them. Remember that the real goal here is to think creatively.

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This week we’re having some fun with probability and a deck of playing cards.

1. You have a deck of 52 cards. Aces take the value one, and face cards take the value 10. You randomly pick a card from the deck, note its value, and return it. You shuffle the deck, and then randomly pick another card. Which is more likely, that the sum of the two card values is even or odd?

2. Let us do the same process, except now we pick four cards, replacing them and shuffling the cards after each pick. What is the probability that the sum of the four cards is even?

3. Taking this a step further, if we pick 100 cards randomly, with replacement, what is the probability that the sum of the 100 cards is even?