An integer is chosen at random from the first two hundred positive integers . What is the probability that the integer chosen is divisible by 6 or 8 ?

Options

A. `1//3`
B. `1//4`
C. `1//5`
D. none of these

Answer

B

Explanation

One integer can be chosen out of 200 integers in `.^(200)C_(1)` ways.
Let A be the event that an integer selected is divisible by 6 and B that it is divisible by 8. Then,
`P(A)=(33)/(200),P(B)=(25)/(200) " and " P(A cap B)=(8)/(192)`
`therefore` Required probability `=P(A cup B)`
`=P(A)+P(B)-P(A cap B)`
`=(33)/(200)+(25)/(200)-(8)/(192)=(1)/(4)`