Calculate the probability of winning 
Suppose you are playing a game where you flip a coin to determine who plays first. You know that when you play first, you win the game 60% of the time and when you play the game second, you lose 52% of the time. A Find the probability that you win the game? 

Let $A = \{ \text{Play first}\}$ and $\overline{A} = \text{Play second}$, let $B = \{ \text{win} \}$
We want $P(B)$.
I know that $P(B | \overline{A}) = 0.48$ and $P(B | A) = 0.6$
Actual problem:
I get that $P(B) = P(B | A)P(A)  + P(B | \overline{A}) P(\overline{A}) = 0.6P(A) + 0.48P(\overline{A})$
I'm not sure how to move ahead. Can someone give me a hint?

Hint:
$$P(A)=\text{chance you get heads at the coin flip}$$
