1) If you roll two sixes on your first try, what are the chances that you will get at least one more six with your next two tries? (Remember it's frequently important to look at the chance of something not happening first.)
2) If you roll a one and a two on your first try, what are the chances that you will get a small straight by the end of your turn? Are the chances any different if you roll a three and a four instead of a one and a two?
3) Next compute the chances of a large straight for #2.
4) In class, we computed the chances of getting Yahtzee on your first try. They aren't very high and it hasn't happened to anyone in our class yet. But we have seen quite a few people getting Yahtzee on the second or third try. In fact, Hannah got it twice in one game. Create a scenario and then compute the chances of getting Yahtzee in that situation. (If you got one yourself, go ahead and do the computation for the scenario that happened to you.)
5) Ivana rolled a 1,2,3,4 and 5 on her first try. Trouble was, she already had a large straight on her score card. She did not yet have a small straight, so she could easily have kept those dice and recorded it as a small straight. Instead, she decided to keep just the 5 and re-roll the four other dice to see if she could get more fives. The decision worked out well for her, because she ended up with a total of four fives and was able to enter those in her fives column up top.
Were the odds in her favor when she made that choice? What did she risk? Is this all just a matter of personal game-playing style, or can you argue that one choice is mathematically superior to the other? Show all computations and label them carefully.
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