A three-digit positive integer is chosen at random. What is the probability that the product of its digits is even?
A. 1/2
B. 31/36
C. 49/54
D. 7/8
E. 11/12
OA B
Source: Manhattan Prep
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 quick way to solve it consists of computing the probability of the complementary event:BTGmoderatorDC wrote: ↑Sun Jun 20, 2021 4:54 pmA three-digit positive integer is chosen at random. What is the probability that the product of its digits is even?
A. 1/2
B. 31/36
C. 49/54
D. 7/8
E. 11/12
OA B
Source: Manhattan Prep
P(three odd digits) \(= \dfrac{5}{9}\cdot \dfrac{5}{10}\cdot \dfrac{5}{10} = \dfrac{5}{36} \)(first digit cannot be \(0,\) so we have a total of \(9\) digits, \(4\) even and \(5\) odd).
Therefore, P(at least one even digit) \(= 1 - \dfrac{5}{36} = \dfrac{31}{36}.\)
Hence, B