Numbers that are palindromes read the same forward and backward. For example, 30203 is a five digit palindrome. If a single number is chosen randomly from the set of all three-digit numbers, find the probability that it will be palindromic.
Answer 1/10??
Yes, that's correct.
Thank you
all possible 3-digit numbers: 100, 101, ... , 999
there are 1000 of them
palindromes:
101, 202, 303, ...909 ---> 9 of those
111, 212, ... 919, --- 9 more
...
191, 292, ... 999 --- 9 of those
so there are 90 of them
prob(of your event) = 90/1000 = 9/100
To find the probability that a randomly chosen three-digit number is palindromic, we need to determine how many three-digit palindromic numbers there are and divide it by the total number of three-digit numbers.
A three-digit palindromic number has the form "ABA", where A and B represent digits. Since A can take any value from 1 to 9 (leading zeros are not allowed in three-digit numbers), there are 9 possible choices for A. Similarly, B can take any value from 0 to 9, giving 10 possible choices for B.
Therefore, the total number of three-digit palindromic numbers is obtained by multiplying the number of choices for A (9) by the number of choices for B (10):
Total number of three-digit palindromic numbers = 9 * 10 = 90
Next, we determine the total number of three-digit numbers. In a three-digit number, the hundreds place can take any value from 1 to 9 (leading zeros are not allowed), and the tens and units places can each take any value from 0 to 9. Hence, there are 9 choices for the hundreds place, and 10 choices for both the tens and units places.
So, the total number of three-digit numbers is obtained by multiplying the number of choices for each place value:
Total number of three-digit numbers = 9 * 10 * 10 = 900
Finally, we can find the probability by dividing the total number of three-digit palindromic numbers by the total number of three-digit numbers:
Probability = (Total number of three-digit palindromic numbers) / (Total number of three-digit numbers)
= 90 / 900
= 1 / 10
Therefore, the probability that a randomly chosen three-digit number is palindromic is 1/10, which means there is a 1 in 10 chance that a randomly chosen three-digit number will be palindromic.