MATH 367, Fall 98, CHAPTER 3 Section 4

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. You have two coins, a fair one and a two–headed one.

(a) If you choose one of the coins at random and then toss it, what is the probability it comes up heads?

(b) If you chose a coin at random, tossed it and came up heads,

what is the probability that you chose the two–headed coin?

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?

For next class: read section 3.4, make a 1 page summary of chapter 3, and do problems 32, 34–39, 41–45, 49–57.