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What is the probability that the units digit of the product of four po

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Bunuel
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What is the probability that the units digit of the product of four po [#permalink] New post  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


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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?
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Re: What is the probability that the units digit of the product of four po [#permalink] New post  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 \(= \frac{2}{5}*\frac{2}{5}*\frac{2}{5}*\frac{2}{5}=(\frac{2}{5})^4=\frac{16}{625}\)

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Re: What is the probability that the units digit of the product of four po [#permalink] New post  03 Feb 2021, 22:03
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)
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CEdward
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Re: What is the probability that the units digit of the product of four po [#permalink] New post  12 Feb 2021, 18:57
Is it just me or did I find this question ambiguous? I thought it was asking what's the probability that the last digit is 1,3,7,9

P(1,3,7,9) = 2/5

The responses above assume that this is a four-digit integer we are looking for (unclear in the stem) and the fact that each integer is 1,3,7,9. In which case I would agree that the probability is

2/5 x 2/5 x 2/5 x 2/5 = 16 / 625

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What is the probability that the units digit of the product of four po [#permalink] New post  18 Jun 2022, 04:26
CEdward

Need to note here..

There are total of 4 positive integers (not necessarily 4-digit positive integers)..

further, For each of the 4 positive integers , the probabilty of finding 1, 3. 7 or 9 as its last digit is 2/5. (ie, selcetion of 1/3/7/9 from 0/1/2/3/4/5/6/7/8//9)

Accordingly, the overall probabilty of selecting such 4 postive integers, with the overall prodct having one amogst 1/3/7/9 will be :-

2/5 * 2/5 * 2/5 * 2/5 = 16/625

Hope it helps..!!
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What is the probability that the units digit of the product of four po [#permalink]
18 Jun 2022, 04:26
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