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!
Probability is a mathematical concept that measures the likelihood of an event occurring. It is important in math because it allows us to make informed decisions and predictions based on the likelihood of different outcomes.
The basic principles of probability include the sample space, event, and probability function. The sample space is the set of all possible outcomes, the event is the specific outcome we are interested in, and the probability function assigns a numerical value to each event to represent its likelihood of occurring.
To calculate probability, we use the formula P(E) = n(E)/n(S), where P(E) is the probability of event E occurring, n(E) is the number of outcomes in event E, and n(S) is the total number of outcomes in the sample space.
Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data from experiments or observations and may differ from theoretical probability due to chance or other factors.
Probability can be applied in various real-life situations, such as predicting the weather, making financial decisions, and analyzing data in scientific experiments. It can also help us understand and evaluate risks and make informed decisions in everyday life.