It is uncertain $($odds are $50-50)$ whether Firm X will enter a new market in the next three months. Firm Y is thinking of entering the same market but won$$t be ready to do so for six months. Firm Y expects to earn $$4$ million if it is the sole market supplier but will lose $$6$ million if it must share the market with Firm X$.$ If Firm X employs an optimal entry strategy, Firm Y$\text{'}$s overall expected profit $($before Firm X has made its move$)$ is: