Question

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

• A. $1-\frac{{30}_{C_2}}{{100}_{C_2}}$
• B. $\frac{{30}_{C_2}}{{100}_{C_2}}$
• C. $\frac{{31}_{C_2}}{{100}_{C_2}}$
• D. $1-\frac{{31}_{C_2}}{{100}_{C_2}}$

Answer 1

The correct option is A $1-\frac{{30}_{C_2}}{{100}_{C_2}}$

No of ways of selecting two number = $100C_2$

Now, no. of ways of selecting two numbers, of which minimum is less than 70 is same as saying subtracting total number of ways of both numbers greater than 70.

$\therefore$ Probability = $1-\frac{30C_2}{100C_2}$ [Total probability =$1$]

(Probability of selecting two object from 30 object to that of 100 object = $\frac{30C_2}{100C_2})$