Probability of Same Last Digit Product of Random Integers

[zorro]

Homework Statement

The probability that two integers chosen at random and their product
will have the same last digit is?

The Attempt at a Solution

According to the given condition, the last digit should be 0,1,5 or 6. Now what is the next step?

 

[Mark44]

Homework Statement

The probability that two integers chosen at random and their product
will have the same last digit is?

The Attempt at a Solution

According to the given condition, the last digit should be 0,1,5 or 6. Now what is the next step?

Is there any information about how large the two integers are?

 

[LCKurtz]

You can't choose two integers "at random", supposedly meaning with equal probability. There are infinitely many integers. You need to specify a probability distribution function.

Also, what given condition? What is special about 0,1,5, and 6?

 

[zorro]

Is there any information about how large the two integers are?

No.

Also, what given condition? What is special about 0,1,5, and 6?

I think you did not understand the question (may be its wording is not correct).
If you select numbers which end with any of the above digits, say 25 and 75, their product 1875 also contains the same last digit '5', which is the required condition.

 

[LCKurtz]

No.



I think you did not understand the question (may be its wording is not correct).
If you select numbers which end with any of the above digits, say 25 and 75, their product 1875 also contains the same last digit '5', which is the required condition.

I still don't understand the question. Apparently you could phrase it as:

"Pick two digits randomly and independently from {0,1,2,...,9}. What is the probability that their product contains the same last digit?"

But what if the two chosen digits are different? What does the "same last digit" mean then?

 

[Mark44]

I still don't understand the question. Apparently you could phrase it as:

"Pick two digits randomly and independently from {0,1,2,...,9}. What is the probability that their product contains the same last digit?"

But what if the two chosen digits are different? What does the "same last digit" mean then?

I would interpret the problem in a similar way, with this revision:

"Pick two digits randomly and independently from {0,1,2,...,9}. What is the probability that the two digits are the same and their product contains the same last digit?"

If that interpretation is correct, then you have 0 * 0 = 0, 1 * 1 = 1, 5 * 5 = 25, and 6 * 6 = 36.

 

[dacruick]

it can be any two integers. How large the number is doesn't matter. If both integers end in a 0, 1, 5, or 6, the conditions will be met. So the first random integer is a 4/10 chance. and the second is a 1/10 chance.

4/10 * 1/10 = 1/25. Therefore there is a 4% chance.

 

[zorro]

it can be any two integers. How large the number is doesn't matter. If both integers end in a 0, 1, 5, or 6, the conditions will be met. So the first random integer is a 4/10 chance. and the second is a 1/10 chance.

4/10 * 1/10 = 1/25. Therefore there is a 4% chance.

Perfect! Thats the answer provided. I understood it now. Thanks!

 

[dacruick]

Perfect! Thats the answer provided. I understood it now. Thanks!

Cheers