Question

# The probability that a two digit number selected at random will be a multiple of '$$3$$' and not a multiple of '$$5$$' is

A
215
B
415
C
115
D
490

Solution

## The correct option is B $$\displaystyle \frac{4}{15}$$$$\Rightarrow$$  Total number of two digit number $$=90$$$$\Rightarrow$$  Total number of two digit number which is divisible by $$3=30$$Out of this there are $$6$$ numbers divisible by $$15$$ $$(15,30,45,60,75,90)$$ which are also divisible by $$5.$$$$\Rightarrow$$  Total two digit number which are divisible by $$3$$ but not $$5=30-6=24$$$$\Rightarrow$$  Required probability $$=\dfrac{24}{90}=\dfrac{4}{15}$$Mathematics

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