Given:
A bowl contains 25 chips numbered 1 to 25.
A chip is drawn randomly from the bowl.
To find:
The probability that it is
a. 9 or 10?
b. even or divisible by 3?
c. divisible by 5 and divisible by 10?
Solution:
a. We have,
Number of total chips = 25
Favorable out comes are either 9 or 10. So,
Number of favorable outcomes = 2
The probability that the selected chip is either 9 or 10 is:
[tex]\text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}[/tex]
[tex]\text{Probability}=\dfrac{2}{25}[/tex]
Therefore, the probability that the selected chip is either 9 or 10 is [tex]\dfrac{2}{25}[/tex].
b. The numbers that are even from 1 to 25 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.
The numbers from 1 to 25 that are divisible by 3 are 3, 6, 9, 12, 15, 18, 21, 24.
The numbers that are either even or divisible by 3 are 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24.
Number of favorable outcomes = 16
The probability that the selected chip is either even or divisible by 3 is:
[tex]\text{Probability}=\dfrac{16}{25}[/tex]
Therefore, the probability that the selected chip is either even or divisible by 3 is [tex]\dfrac{16}{25}[/tex].
c. The numbers from 1 to 25 that are divisible by 5 are 5, 10, 15, 20, 25.
The numbers from 1 to 25 that are divisible by 10 are 10, 20.
The numbers that are divisible by both 5 and 10 are 10 and 20.
Number of favorable outcomes = 2
The probability that the selected chip is divisible by 5 and divisible by 10 is:
[tex]\text{Probability}=\dfrac{2}{25}[/tex]
Therefore, the probability that the selected chip is divisible by 5 and divisible by 10 is [tex]\dfrac{2}{25}[/tex].
