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Chapter 5: Q. 53 (page 329)
Union and intersection Suppose A and B are two events such that P (A), P (B), and
P (A鈭狟). Find P (A鈭〣).
The Pis.
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Bull鈥檚-eye! In a certain archery competition, each player continues to shoot until he or she misses the center of the target twice. Quinn is one of the archers in this competition. Based on past experience, she has a probability of hitting the center of the target on each shot. We want to design a simulation to estimate the probability that Quinn stays in the competition for at least shots. Describe how you would use each of the following chance devices to perform one trial of the simulation.
a. Slips of paper
b. Random digits table
c. Random number generator
What is the probability that the person owns a Dodge or has four-wheel drive?
The two-way table summarizes data on whether students at a certain high school eat
regularly in the school cafeteria by grade level.
a. If you choose a student at random, what is the probability that the student eats
regularly in the cafeteria and is not a grader?
b. If you choose a student at random who eats regularly in the cafeteria, what is the probability that the student is a grader?
c. Are the events 鈥�grader鈥� and 鈥渆ats regularly in the cafeteria鈥� independent?
Justify your answer.
Four-sided dice A four-sided die is a pyramid whose four faces are labeled
with the numbers and(see image). Imagine rolling two fair, four-sided dice and
recording the number that is showing at the base of each pyramid. For instance, you would
record a if the die landed as shown in the figure.
a. Give a probability model for this chance process.
b. Define event A as getting a sum of . Find P(A).
Rock smashes scissors Almost everyone has played the game rock-paper-scissors at some point. Two players face each other and, at the count of , make a fist (rock), an extended hand, palm side down (paper), or a 鈥淰鈥� with the index and middle fingers (scissors). The winner is determined by these rules: rock smashes scissors; paper covers rock; and scissors cut paper. If both players choose the same object, then the game is a tie. Suppose that Player and Player are both equally likely to choose rock, paper, or scissors. a. Give a probability model for this chance process. b. Find the probability that Player wins the game on the first throw .
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