An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is

Options

A. 2,4 or 8
B. 3,6, or 9
C. 4 or 8
D. 5 or 10.

Answer

D

Explanation

We have, `P(A)=(4)/(10)=(2)/(5)`
Suppose B has n outcomes. Then, `P(B)=(n)/(10), 0 lt n lt 10`.
Since A and B are independent events.
`therefore P(A cap B)=P(A)P(B)`
`implies P(A cap B)=(2)/(5)xx(n)/(10)=(2n//5)/(10)`
`implies (2n)/(5)` is an integer between 0 ans 10
`implies (n)/(5)` is an integer between 0 and 5
`implies n=5, 10`.