BrainTwister #44: Dice and cards

#44 Dice and cards

Set by Christopher Dearlove

On each turn of a game, we roll three standard dice with faces numbered 1 to 6 and add up the numbers shown. What is the average (mean) value of that total over a long game?

Now suppose instead of rolling dice, we draw three cards from a six-card deck where the cards are numbered 1 to 6. If we put each card back after drawing it and shuffle before drawing another card, does this change the expected value?

If we instead draw three cards without replacement (so the probabilities are no…