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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
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B
415
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C
115
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D
490
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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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