Question

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.

Answer 1

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

Answer 2

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)?

Answer 3

2/5 ?

Answer 4

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

Answer 5

I still cant get ur hint

Answer 6

=]

Answer 7

i m depressed

Answer 8

hahahaha

Answer 9

im actually laughing irl rn

Answer 10

dang mathmate wrong something huge, can i just do it over

Answer 11

wrote*

Answer 12

6 numbers multiplied together no even, no 5 on the end

Answer 13

is it =2/5 *6

Answer 14

so no even numbers picked, and no 5 picked as that will gurantee a 5 or even number ending

Answer 15

the multiplication of all odd numbers is always off so u are safe there

Answer 16

odd*

Answer 17

answer was (0.4)^6

Answer 18

actuallyi m poor in english , cant totaly understand matemate paragraph

Answer 19

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

Answer 20

the explaination is still same as above

Answer 21

what language do you speak?

Answer 22

rural marathi/hindi

Answer 23

हॅलो दान

Answer 24

https://www.youtube.com/watch?v=GHEX2RrY-cY

Answer 25

okay okay

Answer 26

do u want to start over?

Answer 27

how come \( (10^6/6!)\)

Answer 28

thats all the possible 6 digit products there are

Answer 29

this is another way to think about it uhh

Answer 30

u know we can pick only 4 digits out of the 10 digits

Answer 31

so (4/10)^6

Answer 32

but why ^{6}

Answer 33

for 6 digits