1. Suppose You Flip a Fair Coin Three Times

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1680.010 Chapter 13 Homework Due Monday, 10/8/07

1. Suppose you flip a fair coin three times. a) What is the probability that the first flip is heads?

b) What is the probability that the second flip is tails?

c) What is the probability that the third flip is heads?

d) What is the probability that the first flip is heads, the second is tails, and the third is heads?

e) What is the probability that the first flip is tails, the second flip is tails, and the third flip is heads?

2. Three cards are dealt off the top of a well-shuffled standard deck of cards. a) What is the probability that the first card is a heart?

b) Given that the first card is a heart, what is the probability that the second card is a spade?

c) Given that the first was a heart and the second is a spade, what is the probability that the third is another heart?

d) What is the probability that the first card is a heart, the second card is a spade, and the third card is a heart? 3. Alice and Bob play a game where they each take a well-shuffled standard deck of cards and draw one card off the top of it, without replacement. The one with the highest card wins (aces count as one, Jacks as 11, Queens as 12, and Kings as 13). If the cards have the same value, no one wins. a) If Alice draws first and draws a King, what is the probability that Bob will win?

b) If Alice draws first and draws a 7, what is the probability that Bob will win?

4. Each time a shopper buys toothpaste, he chooses either Brand X or Brand Y. Suppose that, for the first month, he flips a fair coin to decide whether to buy Brand X or Brand Y. Also, for each purchase after the first, the probability that he buys the same brand is 3/5, and the probability that he switches brands is 2/5. What is the probability that his first and second purchases will be Brand X and his third and fourth purchases will be Brand Y? (Hint: Think about what the probability of him buying Brand X the first month is, then the probability of buying it again the second month, and so on.)

5. A Texas clock company owns two factories, one in Dallas and one in Fort Worth. The Fort Worth factory makes 70% of their clocks, and 5% of their clocks are defective. However, 2% of the Dallas clocks are defective. If you go shopping and buy a clock from this company, what is the probability that you buy a defective clock? (Hint: You need to split this up into two problems: The probability that your clock is from Dallas and is defective PLUS the probability that your clock is from Fort Worth and is defective.) 6. a) If two fair 6-sided dice are rolled, what is the probability that both numbers will be the same?

b) If three fair 6-sided dice are rolled, what is the probability that all three numbers will be the same?

7. Suppose that for a particular archer practicing her skills, the probability that her arrow hits the bullseye is 0.6. She shoots four arrows in her practice. a) What is the probability that all four arrows miss the bullseye?

b) What is the probability that at least one will hit the bullseye? (Think about part a)

8. A standard roulette wheel has 38 slots: 18 red, 18 black, and 2 green. A ball is dropped into the wheel while it is spinning. a) What is the probability the ball drops into a red slot?

b) What is the probability the ball does not drop into a red slot?

c) What is the probability the ball drops into a red or black slot?

9. In the game of BINGO, there are 60 balls marked with letters and numbers. The balls marked with a “B” have numbers 1-12, those with an “I” have numbers 13-24, and so on. The balls are drawn randomly without replacement. a) What is the probability that the first ball drawn has a “G” on it?

b) What is the probability that the first ball drawn has an even number on it?

c) What is the probability that the first ball drawn has a “B” on it and is odd?