If any four numbers are selected,what is the | vedclass

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(C) The last digit of a product depends only on the last digits of the individual numbers.For any single number,the possible last digits are $\{0, 1,

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$\frac{16}{625}$

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(C) The last digit of a product depends only on the last digits of the individual numbers.For any single number,the possible last digits are $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$,so there are $10$ possibilities.For the product of four numbers to have a last digit of $1, 3, 5$ or $7$,each of the four numbers must have a last digit from the set $\{1, 3, 5, 7\}$.The probability that a single number has a last digit in $\{1, 3, 5, 7\}$ is $P = \frac{4}{10} = \frac{2}{5}$.Since the four numbers are selected independently,the probability that all four have a last digit in $\{1, 3, 5, 7\}$ is $\left(\frac{2}{5}\right)^4 = \frac{16}{625}$.

If any four numbers are selected,what is the probability that the last digit of their product will be $1, 3, 5$ or $7$?

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