The problem involves determining the probability that the product of two randomly chosen integers will have the same last digit. The discussion centers around the significance of specific last digits (0, 1, 5, or 6) and the implications of selecting integers at random.
The discussion includes various interpretations of the problem, with some participants questioning the clarity of the wording. There are attempts to rephrase the problem for better understanding, and some guidance is offered regarding the selection of integers and their last digits.
Participants note the lack of information about the size of the integers and the need for a probability distribution function for a more precise analysis. There is also a mention of the potential confusion regarding the meaning of "same last digit" in the context of different chosen digits.
Is there any information about how large the two integers are?Abdul Quadeer said: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 said:Is there any information about how large the two integers are?
LCKurtz said:Also, what given condition? What is special about 0,1,5, and 6?
Abdul Quadeer said: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 would interpret the problem in a similar way, with this revision:LCKurtz said: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?
dacruick said: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.
Abdul Quadeer said:Perfect! Thats the answer provided. I understood it now. Thanks!