An integer is chosen at random from first 200 positive integers. Find the probability that the integer is divisible by 6 or 8.

Options

A. `(1)/(4)`
B. `(2)/(4)`
C. `(3)/(4)`
D. None of these

Answer

A

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 nn B)=(8)/(200)`
`therefore P(A uu B)=P(A)+P(B)-P(A nn B)`
`= (33)/(200)+(25)/(200)-(8)/(200)=(1)/(4)`