Multiple choice

Four whole numbers taken at random are multiplied together. What is the chance that the last digit in the product is $1,3,7$ or $9?$

  1. $\displaystyle \frac { 16 }{ 625 } $
  2. $\displaystyle \frac { 1 }{ 210 } $
  3. $\displaystyle \frac { 8 }{ 125 } $
  4. $\displaystyle \frac { 4 }{ 25 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The last digit of a product of four numbers depends only on the last digits of the individual numbers. There are 10 possibilities (0-9) for each digit. The probability that the last digit is 1, 3, 7, or 9 is 4/10 = 2/5 for one number. For four numbers, the probability is (2/5)^4 = 16/625.

AI explanation

For the product of four numbers to end in 1, 3, 7, or 9, every number must end in an odd digit that is not 5. The probability of a number ending in 1, 3, 7, or 9 is 4/10. Using the multiplication rule for independent events, the combined probability is (4/10)^4. This evaluates to 256/10000, which simplifies to 16/625.

Keep practicing — related questions