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### 45-733 PROBABILITY AND STATISTICS I

Practice Conditional Probability Problems From Past Exams and Class Examples

1. Suppose we have three urns. Urn I has 50 red balls, 40 white, and 10 green. Urn II has 20 red balls, 60 white, and 20 green. Urn III has 30 red balls, 30 white, and 40 green. We draw a card randomly from a deck of 52 cards. If the card drawn is a spade we randomly draw 4 balls from Urn I. If the card drawn is a heart or a diamond, we randomly draw 4 balls from Urn II. If the card drawn is a club we randomly draw 4 balls from Urn III. If 2 green and 2 white balls were drawn, what is the probability they came from Urn I?

2. Suppose we have two urns. Urn I contains 12 green balls, 16 yellow, and 2 red. Urn II contains 6 green balls, 5 yellow, and 4 red. We flip a coin. If a head we draw one ball randomly from Urn I, if a tail we draw one ball randomly from Urn II. Given that a yellow ball is drawn, what is the probability that it came from Urn II. Given that a red ball is drawn, what is the probability it came from Urn I?

3. A high ranking U.S. official feels that the probability is .3 that a particular country will devalue its currency in the next six months. A news report is then received that the devaluation will occur. In the past, such news reports have been received before 70 percent of the actual devaluations and before 25 percent of rumored devaluations that did not, in fact, occur. Given the information in the news report, calculate the probability the official should now assign to the likelihood of a devaluation?