What is the probability that a number chosen between 1 and 26 is divisible by 2 or 3?
It is not hard to list and count the numbers form 1 to 26 which divide by 2 or 3
Let me know what you got.
the complement of an 81 degrees angle is
10/13
I disagree
the numbers that are either divisible by 2 or 3 are
2 3 4 6 8 9 10 12 14 15 16 18 20 21 22 24 26
I count 17
so prob = 17/26
But what about the numbers that are divisi ble by both 2 and 3?
No number are divisible by both 2 and 3
To find the probability that a number chosen between 1 and 26 is divisible by 2 or 3, we first need to determine how many numbers in that range are divisible by 2 or 3 and then divide that number by the total possible outcomes.
Step 1: Count the numbers divisible by 2 or 3:
We can determine the number of integers between 1 and 26 that are divisible by 2 or 3 by checking each number one by one or by using an efficient method called the inclusion-exclusion principle.
- Counting the numbers divisible by 2:
Between 1 and 26, there are 13 even numbers (2, 4, 6, ..., 24, 26). So, exactly half (13/26) of the numbers are divisible by 2.
- Counting the numbers divisible by 3:
Between 1 and 26, there are 8 numbers divisible by 3 (3, 6, 9, ..., 24).
However, we need to be careful not to count the numbers divisible by both 2 and 3 twice. These numbers are the multiples of 6: 6, 12, 18, and 24. Therefore, we subtract the count of these numbers from the total.
- Counting the numbers divisible by both 2 and 3 (multiples of 6):
Between 1 and 26, there are 4 numbers that are multiples of 6.
So, the total count of numbers divisible by 2 or 3 is (13 + 8 - 4) = 17.
Step 2: Calculate the probability:
The total number of possible outcomes is the range from 1 to 26, which contains 26 numbers.
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
= 17 / 26
≈ 0.654
Therefore, the probability that a number chosen between 1 and 26 is divisible by 2 or 3 is approximately 0.654 or 65.4%.