Question

In 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.

• Part (a)
  What was Renate's chance of winning a Green Card? Write your answer as a probability statement. (Round your answer to four decimal places.)
  P

•   

• =

• Part (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? Let F = was a finalist. Write your answer as a conditional probability statement. (Round your answer to four decimal places.)
  P

•    

•    

• =

• Part (c)
  Are G and F independent or dependent events? Explain.

• G and F are dependent because becoming a finalist depends on whether or not a person received a Green Card.

• G and F are independent events because the probability of receiving a Green Card does not change if the person becomes a finalist.    

• G and F are dependent events.
  P(G | F)
  and
  P(F)
  when multiplied together give
  P(G).
  G and F are independent because
  P(G AND F)
  can be found by calculating
  P(G) × P(F).

• Part (d)
  Are G and F mutually exclusive events? Explain.
  G and F are mutually exclusive because becoming a finalist and receiving a Green Card cannot occur together.

• G and F are mutually exclusive because becoming a finalist will not allow a person to receive a Green Card.   

• G and F are mutually exclusive because if you are not a finalist, then you cannot receive a Green Card.

• G and F are not mutually exclusive because you could be a finalist and also win a Green Card.

Answer 1

a)

P(G) = 55000/(6.5*10^6) = 0.0085

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