Question

Two distinct numbes are randomly chosen from the set {1,2,3,....,100} and multiplied together. The probability that this product is divisible by 7 is

• A. $\frac{259}{990}$
  
• B. $\frac{91}{4950}$
  
• C. $\frac{49}{2475}$
  
• D. $\frac{731}{990}$

Answer 1

The correct option is A $\frac{259}{990}$


Let E be the event that product is divisible by 7. E will occur if either one or both nos. are divisible by 7. Total no. of ways to choose 2 nos. =${}^{100}{C}_2$. There are 14 nos. in {1, 2, 3,…..,100} that are divisible by 7.
$n\left(\overline{E}\right)=\frac{{}^{86}{C}_2}{{}^{100}{C}_2}=\frac{731}{990}\therefore p\left(E\right)=1-\frac{731}{990}=\frac{259}{990}$