Question
Jamila wrote the numbers 1-100 and placed them in a bag. If she selects a number without without looking what is the probability that number is divisible by 5
Answers
Answered by
GPT-4o mini
To find the probability that a randomly selected number from the set of numbers 1 to 100 is divisible by 5, we can follow these steps:
1. **Count the total numbers**: The total number of integers from 1 to 100 is 100.
2. **Count the numbers divisible by 5**: The numbers divisible by 5 between 1 and 100 can be found by listing them: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100.
Alternatively, we can determine how many integers are there by finding the largest multiple of 5 within 100, which is 100, and using the formula for the nth term of an arithmetic series:
- The nth term of the sequence of numbers divisible by 5 can be described as \(5n\) where \(n\) is a positive integer.
- The largest \(n\) such that \(5n \leq 100\) is \(n = 20\) (since \(5 \times 20 = 100\)).
Thus, the numbers divisible by 5 from 1 to 100 are: \(5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100\), giving us a total of **20** numbers.
3. **Calculate the probability**: The probability \(P\) of selecting a number divisible by 5 is given by the ratio of favorable outcomes to total outcomes:
\[
P(\text{divisible by 5}) = \frac{\text{Number of favorable outcomes (divisible by 5)}}{\text{Total number of outcomes}}
\]
Substituting the values we have:
\[
P(\text{divisible by 5}) = \frac{20}{100} = \frac{1}{5}
\]
Therefore, the probability that a randomly selected number from 1 to 100 is divisible by 5 is \(\frac{1}{5}\) or 0.2.
1. **Count the total numbers**: The total number of integers from 1 to 100 is 100.
2. **Count the numbers divisible by 5**: The numbers divisible by 5 between 1 and 100 can be found by listing them: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100.
Alternatively, we can determine how many integers are there by finding the largest multiple of 5 within 100, which is 100, and using the formula for the nth term of an arithmetic series:
- The nth term of the sequence of numbers divisible by 5 can be described as \(5n\) where \(n\) is a positive integer.
- The largest \(n\) such that \(5n \leq 100\) is \(n = 20\) (since \(5 \times 20 = 100\)).
Thus, the numbers divisible by 5 from 1 to 100 are: \(5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100\), giving us a total of **20** numbers.
3. **Calculate the probability**: The probability \(P\) of selecting a number divisible by 5 is given by the ratio of favorable outcomes to total outcomes:
\[
P(\text{divisible by 5}) = \frac{\text{Number of favorable outcomes (divisible by 5)}}{\text{Total number of outcomes}}
\]
Substituting the values we have:
\[
P(\text{divisible by 5}) = \frac{20}{100} = \frac{1}{5}
\]
Therefore, the probability that a randomly selected number from 1 to 100 is divisible by 5 is \(\frac{1}{5}\) or 0.2.