Question 116775
Let's number the people clockwise 1,2,3 & 4 and have them roll in order.
1 can roll whatever he wants. His chance at the correct number is 6/6.
2 can roll anything but what 1 rolls. His chance at the correct number is 5/6.
3 can roll anything but what 2 rolls. His chance at the correct number is 5/6.
4 can roll anything but what 1 and 3 roll. They will roll different numbers 5/6 of the time and his chance will be 4/6. 1/6 of the time 1 and 3 will roll the same number and his chance will be 5/6.
We must multiply 4/6 * 5 and add 5/6 =25/6 and then divide by 6 for an average.
25/6*1/6=25/36 probability that 4 will roll anything other than what 1 and 3 rolls.
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(5/6)^3*25/36=3125/7776= .401878... Probability that no two people sitting next to each other will roll the same number after they each roll the die once.
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There is no way to check these problems except by a computer program with a good random number generator, so I hope I'm right.
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Ed