Quiz: Conditional Probability

In a promotion at a store, each customer gets a chance to randomly draw a ticket from a box. There are 100 tickets. 20 tickets say “Winner!” and 80 tickets say “Sorry. Try again next time.” Assume two customers play and that the ticket is NOT replaced after the first customer plays. Use this data for questions 1 through 4.

1. What is the probability that the second customer wins, given that the first customer wins?
a. 1/5
b. 19/99
c. 19/100
2. What is the probability that the second customer loses, given that the first customer wins?
a. 4/5
b. 79/99
c. 80/99
3. What is the probability that the second customer wins, given that the first customer loses?
a. 1/5
b. 19/99
c. 20/99
4. What is the probability that the second customer loses, given that the first customer loses?
a. 4/5
b. 79/99
c. 80/99

In a city where it rains frequently, records have been kept and relative frequencies have been used to estimate these probabilities. The probability that rain is predicted on a day is 0.2. The probability that it actually rains on a day that rain is predicted is 0.9. The probability that it actually rains on a day that rain is not predicted is 0.3. Use this data for questions 5 through 9.

5. For a randomly selected day, what is the probability that rain is predicted and it does rain?
a. 0.18
b. 0.2
c. 0.24
6. For a randomly selected day, what is the probability that rain is not predicted and it does rain?
a. 0.18
b. 0.24
c. 0.3
7. For a randomly selected day, what is the probability that it does rain?
a. 0.18
b. 0.24
c. 0.42
8. For a randomly selected day, what is the probability that rain is not predicted, and it does not rain?
a. 0.24
b. 0.56
c. 0.7
9. For a randomly selected day, what is the probability that the prediction is correct?
a. 0.18
b. 0.56
c. 0.74

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