Suppose you play a game with a friend that involves rolling a standard six-sided die. Before a player can participate in the game, he or she must roll a six with the die. As- sume that you roll first and that you and your friend take alternate rolls. In this exercise we will determine the probability that you roll the first six. a. Explain why the probability of rolling a six on any single roll (including your first

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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b. If you don't roll a six on your first turn, then in order for you to roll the first six on
your second turn, both you and your friend had to fail to roll a six on your first
turns, and then you had to succeed in rolling a six on your second turn. Explain
why the probability of this event is
5
000-0*0.
5
c. Now suppose you fail to roll the first six on your second turn. Explain why the
probability is
6
00000-00
6
you to roll the first six on your third turn.
that
d. The probability of you rolling the first six is the probability that you roll the first
six on your first turn plus the probability that you roll the first six on your second
turn plus the probability that your roll the first six on your third turn, and so on.
Explain why this probability is
4
1 5
5
↓ + ( )* (!) + ( )* (!) +
6
Find the sum of this series and determine the probability that you roll the first
six.
Transcribed Image Text:b. If you don't roll a six on your first turn, then in order for you to roll the first six on your second turn, both you and your friend had to fail to roll a six on your first turns, and then you had to succeed in rolling a six on your second turn. Explain why the probability of this event is 5 000-0*0. 5 c. Now suppose you fail to roll the first six on your second turn. Explain why the probability is 6 00000-00 6 you to roll the first six on your third turn. that d. The probability of you rolling the first six is the probability that you roll the first six on your first turn plus the probability that you roll the first six on your second turn plus the probability that your roll the first six on your third turn, and so on. Explain why this probability is 4 1 5 5 ↓ + ( )* (!) + ( )* (!) + 6 Find the sum of this series and determine the probability that you roll the first six.
7. Suppose you play a game with a friend that involves rolling a standard six-sided die.
Before a player can participate in the game, he or she must roll a six with the die. As-
sume that you roll first and that you and your friend take alternate rolls. In this exercise
we will determine the probability that you roll the first six.
a. Explain why the probability of rolling a six on any single roll (including your first
turn) is.
Transcribed Image Text:7. Suppose you play a game with a friend that involves rolling a standard six-sided die. Before a player can participate in the game, he or she must roll a six with the die. As- sume that you roll first and that you and your friend take alternate rolls. In this exercise we will determine the probability that you roll the first six. a. Explain why the probability of rolling a six on any single roll (including your first turn) is.
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