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mathmath333

  • one year ago

6 positive number are taken at random and multiplied together. Then what is the probability that the product ends in an odd digit other than 5.

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{ 6 positive number are taken at random and multiplied together.}\hspace{.33em}\\~\\ & \normalsize \text{ Then what is the probability that the product ends in an odd }\hspace{.33em}\\~\\ & \normalsize \text{ digit other than 5. }\hspace{.33em}\\~\\ \end{align}}\)

  2. mathmate
    • one year ago
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    I assume "random" means that the probability of the last digit is uniformly distributed over the range 0-9. The resulting last digit depends only on the last digit of the six numbers, so without loss of generality (WLOG), we will consider only the product of six "random" digits. The resulting digit will be odd if and only if all six digits are odd. So what is the probability of getting 6 odd digits out of a uniform distribution? Out of the set {0,1,2,3,4,5,6,7,8,9}, there are 5 odd digits. So the probability of randomly selecting an odd digit is 5/10=1/2, resulting in an odd number. However, we know that 5 multiplied by any odd number will have 5 as a terminating digit, so we need to exclude 5 in ALL of the six numbers. That leaves us with 4, A={1,3,7,9} to choose from (out of 10). The probability of choosing any element of A from 10 digits is 4/10=2/5. The experiment is a 6 step experiment, each one independent of each other, so the multiplication rule applies. Can you figure out the probability of the final result (terminating with an odd digit excluding 5)?

  3. mathmath333
    • one year ago
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    2/5 ?

  4. mathmate
    • one year ago
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    It's 2/5 if you only pick one single number. Use the multiplication rule for 6 numbers that are multiplied together.

  5. mathmath333
    • one year ago
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    I still cant get ur hint

  6. dan815
    • one year ago
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    =]

  7. mathmath333
    • one year ago
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    i m depressed

  8. dan815
    • one year ago
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    hahahaha

  9. dan815
    • one year ago
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    im actually laughing irl rn

  10. dan815
    • one year ago
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    dang mathmate wrong something huge, can i just do it over

  11. dan815
    • one year ago
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    wrote*

  12. dan815
    • one year ago
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    6 numbers multiplied together no even, no 5 on the end

  13. mathmath333
    • one year ago
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    is it =2/5 *6

  14. dan815
    • one year ago
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    so no even numbers picked, and no 5 picked as that will gurantee a 5 or even number ending

  15. dan815
    • one year ago
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    the multiplication of all odd numbers is always off so u are safe there

  16. dan815
    • one year ago
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    odd*

  17. mathmath333
    • one year ago
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    answer was (0.4)^6

  18. mathmath333
    • one year ago
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    actuallyi m poor in english , cant totaly understand matemate paragraph

  19. dan815
    • one year ago
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    hence we have 4 choices for each of the places so 4^6/6!, as we dont care about the order u pick the 6 numbers so (4^6/6!) / (10^6/6!) = 0.4^6

  20. dan815
    • one year ago
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    the explaination is still same as above

  21. dan815
    • one year ago
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    what language do you speak?

  22. mathmath333
    • one year ago
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    rural marathi/hindi

  23. mathmath333
    • one year ago
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    हॅलो दान

  24. mathmath333
    • one year ago
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    https://www.youtube.com/watch?v=GHEX2RrY-cY

  25. dan815
    • one year ago
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    okay okay

  26. dan815
    • one year ago
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    do u want to start over?

  27. mathmath333
    • one year ago
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    how come \( (10^6/6!)\)

  28. dan815
    • one year ago
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    thats all the possible 6 digit products there are

  29. dan815
    • one year ago
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    this is another way to think about it uhh

  30. dan815
    • one year ago
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    u know we can pick only 4 digits out of the 10 digits

  31. dan815
    • one year ago
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    so (4/10)^6

  32. mathmath333
    • one year ago
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    but why ^{6}

  33. dan815
    • one year ago
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    for 6 digits

  34. dan815
    • one year ago
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    |dw:1444592494691:dw|

  35. dan815
    • one year ago
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    tbh we shudnt even be thinking of just 10 digits lol

  36. dan815
    • one year ago
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    its the fact that 4/10 of an infinite possible positive numbers

  37. mathmath333
    • one year ago
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    ok

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