please help!
1.) A random digit from 1 to 9 (inclusive) is chosen, with all digits being equally likely. The probability that when it's squared it will end with the digit 1.
2.) A random number between 1 and 20 (inclusive) is chosen. The probability that its square root will not be an integer.
1. Find how many (initial) digits when squared gives one. Dividing that by 9 will give you the required probability.
Also, it may be of interest to note that single digits that add up to 10 have the same last digits when squared.
Example: 2²=4 8²=(10-2)²=64 also ends with the digit 4.
2. Again, determine how many "perfect squares" there are among the numbers 1 to 20. Divide that number by 20 will give you the probability.
Sure, I can help you with that!
1.) The probability that a random digit from 1 to 9, when squared, will end with the digit 1 can be found by analyzing the possible outcomes. The only digits between 1 and 9 which will give a square ending with 1 are 1, 3, 7, and 9. The digits that end with 1 when squared are 1 and 9. Therefore, the probability is 2/9, since there are a total of 9 possible outcomes (digits from 1 to 9) and 2 of them satisfy the condition.
2.) To find the probability that the square root of a random number between 1 and 20 (inclusive) will not be an integer, we need to determine the number of outcomes that satisfy this condition.
The only numbers between 1 and 20 whose square roots are not integers are those whose square roots are irrational. The irrational square roots between 1 and 20 are √2, √3, √5, √6, √7, √8, √10, √11, √12, √13, √14, √15, √17, √18, and √19.
Counting these numbers, we have a total of 15 square roots that are not integers. Therefore, the probability is 15/20, which simplifies to 3/4.
I hope this helps! Let me know if you have any further questions.
Sure, I'll be happy to help you with these questions!
1.) To determine the probability that a random digit from 1 to 9 (inclusive) when squared will end with the digit 1, we need to find the number of favorable outcomes and the total number of outcomes.
Let's first determine the favorable outcomes. In the given range, the digits that, when squared, end with the digit 1 are 1, 4, and 9.
Next, we need to find the total number of outcomes, which is simply the number of digits in the given range, which is 9.
Therefore, the probability is the number of favorable outcomes divided by the total number of outcomes. In this case, it is 3 (favorable outcomes) divided by 9 (total outcomes), which simplifies to 1/3. So, the probability is 1/3.
2.) To find the probability that a random number between 1 and 20 (inclusive) has a square root that is not an integer, we need to identify the favorable outcomes and the total outcomes.
The favorable outcomes are the numbers whose square roots are not integers. In the given range, the numbers with non-integer square roots are 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, and 20.
The total number of outcomes is the total number of numbers in the given range, which is 20.
Therefore, the probability is the number of favorable outcomes divided by the total number of outcomes. In this case, it is 16 (favorable outcomes) divided by 20 (total outcomes), which simplifies to 4/5. So, the probability is 4/5.