Two numbers a and b are selected ar random from 1, 2, ,3,.., 100 and a multipied. Then, the probability that the product ab is divisible by 3, is

Options

A. `(67)/(150)`
B. `(83)/(150)`
C. `(67)/(75)`
D. `(8)/(75)`

Answer

B

Explanation

Two numbers can be chosen out of first 100 natural numbers in `.^(100)C_(2)`
The product ab is divisble by 3 if at least one of the two numbers is divisible by 3.
`therefore` Required probability
=1- Probability that none of the two numbers chosen is divisble by 3.
`=1-(.^(67)C_(2))/(.^(100)C_(2))=1-(67xx33)/(50xx99)=1-(67)/(150)=(83)/(150)`