MCQ
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 $9\,p$ is equal to.
- A$1.0146$
- B$1.2085$
- ✓$1.0285$
- D$1.1521$
✓
Answer
Correct option: C.
$1.0285$
c
Sol. $n ( S )=$ all 5 digit nos $=9 \times 10^{4}$
Sol. $n ( S )=$ all 5 digit nos $=9 \times 10^{4}$
$A :$ no is multiple of $7$ but not divisible by $5$
Smallest $5$ digit divisible by $7$ is $10003$
Largest $5$ digit divisible by $7$ is $99995$
$\therefore 99995=10003+( n -1) 7 \quad n =12857$
Numbers divisible by $35$
$99995=10010+( P -1) 35 \Rightarrow P =2572$
$\therefore$ Numbers divisible by $7$ but not by $35$ are
$12857-2572=10285$
$\therefore P =\frac{10285}{90000}$
$\therefore 9\,P =1.0285$
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