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

mathmate
 one year ago
Best ResponseYou've already chosen the best response.6I assume "random" means that the probability of the last digit is uniformly distributed over the range 09. 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)?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.6It's 2/5 if you only pick one single number. Use the multiplication rule for 6 numbers that are multiplied together.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1I still cant get ur hint

dan815
 one year ago
Best ResponseYou've already chosen the best response.2im actually laughing irl rn

dan815
 one year ago
Best ResponseYou've already chosen the best response.2dang mathmate wrong something huge, can i just do it over

dan815
 one year ago
Best ResponseYou've already chosen the best response.26 numbers multiplied together no even, no 5 on the end

dan815
 one year ago
Best ResponseYou've already chosen the best response.2so no even numbers picked, and no 5 picked as that will gurantee a 5 or even number ending

dan815
 one year ago
Best ResponseYou've already chosen the best response.2the multiplication of all odd numbers is always off so u are safe there

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1answer was (0.4)^6

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1actuallyi m poor in english , cant totaly understand matemate paragraph

dan815
 one year ago
Best ResponseYou've already chosen the best response.2hence 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

dan815
 one year ago
Best ResponseYou've already chosen the best response.2the explaination is still same as above

dan815
 one year ago
Best ResponseYou've already chosen the best response.2what language do you speak?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1rural marathi/hindi

dan815
 one year ago
Best ResponseYou've already chosen the best response.2do u want to start over?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1how come \( (10^6/6!)\)

dan815
 one year ago
Best ResponseYou've already chosen the best response.2thats all the possible 6 digit products there are

dan815
 one year ago
Best ResponseYou've already chosen the best response.2this is another way to think about it uhh

dan815
 one year ago
Best ResponseYou've already chosen the best response.2u know we can pick only 4 digits out of the 10 digits

dan815
 one year ago
Best ResponseYou've already chosen the best response.2tbh we shudnt even be thinking of just 10 digits lol

dan815
 one year ago
Best ResponseYou've already chosen the best response.2its the fact that 4/10 of an infinite possible positive numbers
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