## A three-digit positive integer is chosen at random. What is the probability that the product of its digits is even?

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### A three-digit positive integer is chosen at random. What is the probability that the product of its digits is even?

by Gmat_mission » Sun Jun 13, 2021 10:14 am

00:00

A

B

C

D

E

## Global Stats

A three-digit positive integer is chosen at random. What is the probability that the product of its digits is even?

A. $$\dfrac12$$

B. $$\dfrac{31}{36}$$

C. $$\dfrac{49}{54}$$

D. $$\dfrac78$$

E. $$\dfrac{11}{12}$$

Source: Manhattan GMAT

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### Re: A three-digit positive integer is chosen at random. What is the probability that the product of its digits is even?

by Ian Stewart » Sun Jun 13, 2021 2:03 pm
The product of the digits will only be odd if all three digits are odd. If we want all of our digits to be odd, we'd have 5 choices for each digit, so there will be 5^3 = 125 such three-digit numbers.

For the remaining 900 - 125 = 775 three-digit numbers, the product of the digits will be even. So if we pick one of the 900 three-digit numbers at random, the probability it will have an even product of its digits is 775/900. The numerator and denominator are both divisible by 25, so we can cancel 25, to get 31/36.
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