A five-digit integer will be chosen at random from all possible positive five-digit integers. What is the probability that the number's units digit will be less than 5? Express your answer as a common fraction.
the last digit can be 0,1,2,3 or 4 out of 10 possible digits, so that is 5/10 or 0.5
Suppose that after I wrote this problem, Kev thought he could be more clever than I could, so he wrote his own problem. Suppose that both of our problems are in the set of 12 problems you are currently working on. If you sat down at your computer this morning and randomly loaded 4 of the 12 problems, what is the probability that both this problem and Kev's problem were among the four you loaded?
there are 12C4 ways to chose 4 items from 12, that is the denominator.
We want your 2 problems included and 2 other problems out of the 10 remaining included so
The prob of your 2 problems and two other problems being chosen at random out of 12 is 1*10C2 / 12C4
Put them both together and we get.
\(0.5\times \frac{\binom{10}{2}}{\binom{12}{4}}=0.5\times \frac{45}{495}=\frac{1}{22}\)
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+118735 
