Most Frequently Rolled NumberDate: 10/27/1999 at 21:54:54 From: Zoe Nesbitt Subject: Determining odds If I had two dice each with the following numbers on them: -3, -2, -1, 0, 1, and 2, and rolled them 100 times, what sum would be rolled most often and why? Can you help? Date: 10/28/1999 at 03:29:20 From: Doctor Ian Subject: Re: Determining odds Hi Zoe, Let's look at the case for regular dice, numbered 1-6. Here are the possible sums: second die + 1 2 3 4 5 6 ------------------ 1 | 2 3 4 5 6 7 2 | 3 4 5 6 7 8 first 3 | 4 5 6 7 8 9 die 4 | 5 6 7 8 9 10 5 | 6 7 8 9 10 11 6 | 7 8 9 10 11 12 How often does each sum appear in the table? Sum Appears --- ------- 2 1 time 3 2 times 4 3 times 5 4 times 6 5 times 7 6 times 8 5 times 9 4 times 10 3 times 11 2 times 12 1 time Now, suppose you had 36 balls, and you marked them this way: Mark Number of balls ---- --------------- 2 1 3 2 4 3 5 4 6 5 7 6 8 5 9 4 10 3 11 2 12 1 Put the balls in a hat, and draw one out. Toss it back in, and draw one out again. If you keep doing this, which mark would you expect to draw most often? Do you see why the problem with the dice and the problem with the balls are really just two versions of the same problem? Can you see how this relates to _your_ problem? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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