Two Basic Rules of Probability · Exercise 25

1994, the U.S. government held a lottery to issue 55,000 Green Cards (permits for non-citizens to work legally in the U.S.). Renate Deutsch, from Germany, was one of approximately 6.5 million people who entered this lottery. Let G = won green card.

(a) What was Renate’s chance of winning a Green Card? Write your answer as a probability statement.
(b) In the summer of 1994, Renate received a letter stating she was one of 110,000 finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to win, what was Renate’s chance of winning a Green Card? Write your answer as a conditional probability statement. Let F = was a finalist.
(c) Are G and F independent or dependent events? Justify your answer numerically and also explain why.
(d) Are G and F mutually exclusive events? Justify your answer numerically and explain why.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §3.3 Two Basic Rules of Probability · Exercise 25