Let S be the sample space of all five digit numbers.

Question

Let $S$ be the sample space of all five digit numbers. If $p$ is the probability that a randomly selected number from $S$ is a multiple of 7 but not divisible by 5, then $9p$ is equal to:

Accepted Answer

5-digit numbers divisible by 7: first is $10003$, last is $99995$. Count $=\dfrac{99995-10003}{7}+1=12857$.

5-digit numbers divisible by 35 (7 and 5): first is $10010$, last is $99995$. Count $=\dfrac{99995-10010}{35}+1=2572$.

Divisible by 7 but not 5: $12857-2572=10285$.

Total 5-digit numbers: $90000$.

$$9p = \frac{10285}{90000}\times9 = 1.0285$$

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