Question

Three - digit numbers formed by using digits $0,1,2$ and $5$ (without repetition) are written on different slips with distinct number on each slip, and put in a bowl. One slip is drawn at random from the bowl. The probability that the slip bears a number divisible by $5$ is

• A. $\frac{5}{9}$
• B. $\frac{4}{9}$
• C. $\frac{2}{3}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{5}{9}$

There are $4$ group of three digits and that is $(0,1,2),(0,1,5),(0,2,5),(1,2,5)$

The three digit numbers formed by $(0,1,2),(0,1,5),(0,2,5)$ groups are $12$ ($4$ for each).

The three digit numbers formed by $(1,2,5)$ group is $6$ So, sample space $S=\{120,201,102,210,150,105,501,510,250,520,205,502,125,152,521,512,251,215\}$

$n\left(S\right)=18$

Let $A$ be the event of getting number divisible by $5$

So, $A=\{120,210,150,510,105,250,520,205,125,215\}$

$\therefore n\left(A\right)=10$

$\therefore$ $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{10}{18}=\frac{5}{9}$

Hence, option A is correct.