Q:

Number of outcomes of B

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 .
In this I am not getting any start .
I just know that dor independent $P(A\cap B)=P(A)P(B)$

A:

Hint: If $k$ is the number of outcomes in both $A$ and $B$, we have $P(A \cap B) = \frac{k}{10}$. 
Obviously $P(A) = \frac{4}{10}$. If there are $n$ outcomes in $B$, we have $P(B) = \frac{n}{10}$. 
If $P(A\cap B)=P(A)P(B)$, then $\frac{k}{10} = \frac{4}{10} \frac{n}{10}$.
What integers $0 < k,n \leq 10$ can you choose such that this is true?

