What is the probability that a two digit number chosen at random will be a multiple of 3 and not of 5 .

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- Jan 18th 2009, 10:57 PMmathaddictnumbers + probability
What is the probability that a two digit number chosen at random will be a multiple of 3 and not of 5 .

- Jan 18th 2009, 11:19 PMmr fantastic
- Jan 20th 2009, 10:20 AMSoroban
Hello, mathaddict!

Quote:

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: .$\displaystyle P(\text{multiple of 3, not 5}) \:=\:\frac{24}{90} \:=\:\frac{4}{15}$