Bob is playing a game of chance. It costs him $5 to play. He flips a coin 4 times and guesses its outcome on each flip. For each one he guesses correctly, he receives \$2. What are his expected winnings?
I tried :
Y = net winnings
X = number of correct guesses
The net winning equation I came up with is: $$Y = 2X-5$$
From what, I know that $E(Y)=-5+2E(X)$.
Since X~B(4,1/2), then E(X)=np=2
So in conclusion E(Y)=-1
Can a net winning expectation be - 1?
would that mean he will lose one 1$ on average?
I feel like he wins when he gets a correct bet but that can also be the case when he wins some money. I'm a bit confused and any help would be welcome.