Question

The probability that a two digit number selected at random will be a multiple of ${}^{\prime }{3}^{\prime }$ but not a multiple of ${}^{\prime }{5}^{\prime }$ is

• A. $\frac{7}{15}$
• B. $\frac{1}{3}$
• C. $\frac{4}{15}$
• D. $\frac{2}{5}$

Answer 1

The correct option is C $\frac{4}{15}$

Total number of two-digit number $=90$
$\therefore n\left(S\right)=90$
Total number of two-digit number divisible by $3=30$
Out of these $30$ numbers $(15,30,45,60,75,90)$ are divisible by $5$
$\therefore$ Total number of two digit number divisible by $3$ but not by $5=24$
$\therefore$ Required probability $=\frac{24}{90}=\frac{4}{15}$