Problem of the Day
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Problem of the Day
RoDMaster Wed Jul 20, 2011 4:52 am
I will give you one problem per day to solve with a solution. These problems will come from various high school contests.
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Problem 1
RoDMaster Wed Jul 20, 2011 4:53 am
When five ordinary six-sided dice are tossed simultaneously, the probability that a 1 shows on the
top face of exactly two of the dice is
top face of exactly two of the dice is
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Re: Problem of the Day
ClaudiaFeng Wed Jul 20, 2011 6:54 am
Easy.
5C2 ways to choose which dice have the 1, then (1/6)^2 of getting 2 1's and (5/6)^3 of getting non-1's.
So the probability is 10*125/6^5=1250/7776=625/3888.
5C2 ways to choose which dice have the 1, then (1/6)^2 of getting 2 1's and (5/6)^3 of getting non-1's.
So the probability is 10*125/6^5=1250/7776=625/3888.
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Problem 2
RoDMaster Wed Jul 20, 2011 7:17 am
Let sn = 2 + 1/2! + 1/3! + 1/4! + · · · + 1/n! .
As n gets larger, the difference of sn and which of these
numbers diminishes towards zero?
As n gets larger, the difference of sn and which of these
numbers diminishes towards zero?
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