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. $\frac{2}{15}$
• B. $\frac{4}{15}$
• C. $\frac{1}{15}$
• D. $\frac{4}{90}$

Answer 1

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

$\Rightarrow$ 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 $=\frac{24}{90}=\frac{4}{15}$