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03 Feb 2021, 10:31
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What is the probability that the units digit of the product of four positive integers is 1, 3, 7, or 9 ?
A. 16/625
B. 81/625
C. 2/5
D. 3/5
E. 609/625
Are You Up For the Challenge: 700 Level Questions
A. 16/625
B. 81/625
C. 2/5
D. 3/5
E. 609/625
Are You Up For the Challenge: 700 Level Questions
If 4 whole numbers taken at random are multiplied together, what is the probability that the last digit in the product is 1,3,7 or 9?
03 Feb 2021, 20:48
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Favorable choices \({0,1,2,3,4,5,6,7,8,9}\)
The units digit of the product of four positive integers is \({1, 3, 7, 9}\)
Probability of selecting one number \(P(S)= \frac{4}{10}=\frac{2}{5}\)
Required Probability \(= \frac{2}{5}*\frac{2}{5}*\frac{2}{5}*\frac{2}{5}=(\frac{2}{5})^4=\frac{16}{625}\)
IMO Ans A
The units digit of the product of four positive integers is \({1, 3, 7, 9}\)
Probability of selecting one number \(P(S)= \frac{4}{10}=\frac{2}{5}\)
Required Probability \(= \frac{2}{5}*\frac{2}{5}*\frac{2}{5}*\frac{2}{5}=(\frac{2}{5})^4=\frac{16}{625}\)
IMO Ans A
03 Feb 2021, 22:03
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Product of only positive integers that end 1, 3, 7 and 9 will result a positive integer whose units digit is 1,3,7, or 9. Each of the 4 integers should end in one of the 1, 3, 7, or 9. So we have 4 options for each integer and we can choose the number of integers whose product is an integer whose units digit is 1,3,7, or 9 in 4*4*4*4=256 ways. As there are 10 possible digits, in total, there are 10*10*10*10=10,000 ways of choosing 4 integers. So P(selecting 4 integers whose product will result an integer whose units digit is 1,3,7, or 9)= 256/10,000=16/625 IMA A)
