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A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning heads on the first toss, followed by two tails).   The 8  outcomes are listed below. Assume that each outcome has the same probability.   Complete the following. Write

A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning heads on the first toss, followed by two tails).   The 8  outcomes are listed below. Assume that each outcome has the same probability.   Complete the following. Write

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter0: Preparing For Algebra
Section: Chapter Questions
Problem 71POT
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A coin is tossed three times. An outcome is represented by a string of the sort

HTT

(meaning heads on the first toss, followed by two tails).

 

The

8

 outcomes are listed below. Assume that each outcome has the same probability.

 

Complete the following. Write your answers as fractions.



(a)Check the outcomes for each of the three events below. Then, enter the probability of each event.

 

  Outcomes Probability
 
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
Event A: The first toss is heads
 
 
 
 
 
 
 
 
 
Event B: More heads than tails
 
 
 
 
 
 
 
 
 
Event A and B: The first toss is heads and more heads than tails
 
 
 
 
 
 
 
 
 
 
 
 

 

(b)Suppose the first toss is heads. (That is, Event
A
occurs.) This will limit the possible outcomes. From the remaining outcomes, check the outcomes for Event
B
. Then, enter the probability that Event
B
occurs given that Event
A
occurs.

 

  Outcomes given the first toss is heads Probability
 
HHH
HHT
HTH
HTT
        
Event B: More heads than tails
 
 
 
 
        
 
 
 
 

 

(c)Give the following probabilities and select the correct option below.

 

PA and BPA
=
 
PB|A
=
 
PA and BPA
 ▼?
PB|A
 
 
 
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