Question

From a set of $17$ cards numbered $1$ to $17$ one is drawn at random. The probability that it is divisible by $3$ or $5$ is

• A. $\frac{8}{17}$
• B. $\frac{5}{17}$
• C. $\frac{6}{17}$
• D. $\frac{7}{17}$

Answer 1

The correct option is D $\frac{7}{17}$

The numbers less than or equal to $17$ which are divisible by $3$ are $3,6,9,12,15$.

Similarly, the numbers less than or equal to $17$ which are divisible by $5$ are $5,10,15$.

Numbers less than or equal to $17$ which are divisible by both $3$ and $5$ are $1$.

Hence, total $5+3-1=7$ numbers are divisible by $3$ or $5$.
Total number of cards$=17$
So probability is equal to$=\frac{7}{17}$
The correct option is D.