Multiple choice

If 4 whole numbers taken at random are multiplied together, then the chance that the last digit in the product is 1, 3, 7 or 9 is

  1. $\dfrac{16}{625}$
  2. $\dfrac{4}{125}$
  3. $\dfrac{8}{81}$

  4. none
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A Correct answer
Explanation

The last digit of a product of integers depends only on the last digits of the factors. For the product to end in 1, 3, 7, or 9, each of the 4 factors must be odd and not end in 5. There are 4 such digits (1, 3, 7, 9) out of 10 possible digits for each factor, so the probability is (4/10)^4 = (2/5)^4 = 16/625.

AI explanation

For the product of four randomly selected whole numbers to end in 1, 3, 7, or 9, every single number must end in 1, 3, 7, or 9. Out of the 10 possible last digits (0 through 9), 4 are favorable, making the probability of choosing one such number 4 out of 10, or 2 out of 5. By the multiplication theorem for independent events, the probability that all four numbers end in these digits is (2/5) multiplied by itself four times, which equals 16 divided by 625.

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