Two numbers are selected at random from 1,2,3,…….100 without replacement. Find the probability that the minimum of the two numbers is less than 70.

Since two numbers are selected at random from 1,2,……100 we have,  $n\left(S\right)={}^{100}{C}_2$ Let A be the event that the minimum of the two numbers is less than 70; Then the complement of A i,e.,  $A^c$ is the event of selecting both the numbers from  $(70,71,\mathrm{......100})$

$n\left(A^c\right)={}^{31}{C}_2$

$P\left(A^c\right)=\frac{{ }^{33}{C}_2}{{ }^{100}{C}_2}\Rightarrow P\left(A\right)=1-\frac{{ }^{31}{C}_2}{{ }^{100}{C}_2}=\frac{299}{330}$