Four whole number taken at random are multiplied together. The chance that the last digit of the product is 1, 3, 7, or 9 is ?



Four whole number taken at random are multiplied together. The chance that the last digit of the product is 1, 3, 7, or 9 is ?

A. 16/625

B. 1/210

C. 8/125

D. 4/25

Answer : A. 16/625


Explanation:

  • Since the product has to end in 1, 3, 7 or 9, the units place of all the 4 numbers we want to multiply can't end in 0, 2, 4, 5, 6, 8. That means it can only end in 1, 3, 7, 9.
  • This means that the probability of selecting one number that ends in 1, 3, 7 or 9 is 4/10 = 2/5.
  • Therefore the probability of selecting four numbers that end in 1, 3, 7 or 9 is (2/5) x (2/5) x (2/5) x (2/5) = 16/625.
  • Hence, the probability of selecting 4 numbers such that their product ends in 1, 3, 7 or 9 is 16/625.

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