What is the probability that a two digit number chosen at random will be a multiple of 3 and not of 5 .
Hello, mathaddict!
What is the probability that a two digit-number chosen at random
will be a multiple of 3 and not of 5?
There are 90 two-digit numbers.
One-third of them are mutliples of 3: .$\displaystyle \frac{90}{3} \:=\:30$ multiples of 3.
But every fifth one of them is a multiple of 5: .$\displaystyle \frac{30}{5} \:=\: 6$ multiples of 15.
Hence, there are: .$\displaystyle 30 - 6 \:=\:{\color{blue}24}$ multiples of 3 which are not multiples of 5.
Therefore: .$\displaystyle P(\text{multiple of 3, not 5}) \:=\:\frac{24}{90} \:=\:\frac{4}{15}$