# Understanding these probabilities, and reading the pdf and cdf

UPDATE: this is a math question but as i would like to codify it, I thought the DS SE might be appropriate.

I am trying to sketch out this problem statement. Where am I going wrong since I don't see how they get

• "6% chance of losing any money at all",
• "41% chance of making more than \$100M" and • "75% of earning at least \$40M".

My attempt at a solution is in the second image: Row 48 (CASES) enumerates the number of ways the sum can take a given value, while row 49 (PROB) is that number in row 48 divided by the total number of outcomes. This gives me the pdf and row 50 is the cdf. Yet I don't get the answers in the problem statement. Are they wrong or am I reading the pdf and cdf the wrong way?

The first image is the text below.

The payoff aren't +30 and -10. They're +20 and -10. Successful projects return \$30M after investing \$10M.