13.5: Chapter Exercises
- Page ID
- 95130
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Chapter Exercises
- You roll a pair of dice. Assume that the number that comes up on each die is independent of the number that comes up on the other (which is the case in all normal situations).
- What is the probability that you roll two sixes (“box cars”). Hint: this is a “one-way” point; both dies must come up sixes.
- What is the probability that you roll two ones?
- What is the probability that you not roll a double six?
- What is the probability that you will either roll two sixes or else roll two ones?
- What is the probability that you roll a five?
- What is the probability that you roll a seven or eleven?
- You are going to draw one card from a standard deck of playing cards. Once you see what the card is, you replace it, then draw a second card. Determine the probabilities of each of the following, say which rules are relevant, and explain how you use the rules to obtain the results.
- What is the probability that you get a jack on the first draw?
- What is the probability that you get a diamond on the first draw?
- What is the probability that you get a jack of diamonds on the first draw?
- What is the probability that you get a jack or a diamond on the first draw?
- What is the probability of a queen on the first draw and a jack on the second?
- What is the probability of getting one jack and one queen (here the order in which you get them doesn’t matter)?
- What is the probability of getting two aces?
- What is the probability of drawing exactly one ace?
- What is the probability of getting at least one ace?
- What is the probability of not getting an ace on either draw?
- Pr(P) = 1/2, Pr(Q) = 1/2, and Pr(P & Q) = 1/4.
- Are P and Q incompatible? Why or why not?
- What is the probability of P or Q?
- Consider the following possible outcomes of flipping a coin three times, where H = Head and T = Tail.
HHH, TTT, HTH, THT
You know that if the coin is fair, the probability of all four sets of outcomes is the same: 1/2 x 1/2 x 1/2 = 1/8. Now calculate the probabilities for each of the outcomes when the coin is biased, and the probability of getting a head on any flip is 0.70.
- What is the probability of getting a head on the first flip or on the second when you flip the biased coin described in the previous problem two times?