MATH 367, spg 98, CHAPTER 3 Section 3, Feb 20 Conditional Probability

1. An urn contains 5 Red balls and 3 Blue balls.

(a) Two balls are taken from the urn without replacement. What is the probability that both are Red?

(b) Three balls are taken from the urn without replacement. What is the probability that all three are Red?

(c) Three balls are taken from the urn without replacement. What is the probability that (at least) two balls are Red?

(d) Three balls are taken from the urn without replacement. If two balls are Red, what is the probability that all three balls are Red?

2. What is the probability that all five cards in a poker hand are diamonds?

3. In a television show a contestant is required to throw a die. She then tosses as many coins as there were spots shown in the die. If she throws exactly four heads, she wins $10,000. What is the probability that she wins?

4. At a certain stage of a criminal investigation the inspector in charge is 60% convinced of the guilt of a certain suspect. Suppose now that a new piece of evidence that shows that the criminal has a certain characteristic is uncovered. If 20% of the population has this characteristic, how certain of the guilt of the suspect should the inspector now be if it turns out that the suspect has this characteristic?

For next class: read section 3.3, make a 1 page summary of chapter 3, and do problems 32, 34–39, 41–45, 49–57.