To calculate diluted EPS, we start by adding those diluted shares (50 million + 150 million = 200 million) to the 200 million outstanding shares to get a denominator of 400 million shares. We use the same numerator as before ($100 million) to get a diluted EPS of $0.25/share.
In real life, diluted EPS will seldom deviate so drastically from ordinary EPS. Plus, this is a simplified view of stock options. Stock options can execute at varying strike prices, potentially altering the number of stocks issued and therefore the total number of diluted shares.