   Chapter 7.2, Problem 12E

Chapter
Section
Textbook Problem

# Exercises 7–12 are based on the following table, which shows the frequency of outcomes when two distinguishable coins were tossed 4,000 times and the uppermost faces were observed. [HinT: See Example 2.] Outcome HH HT TH TT Frequency 1,100 950 1,200 750 Would you judge the first coin to be fair? Give a reason for your answer.

To determine

The explanation whether the first coin is fair for the frequency of outcomes when two distinguishable coins were tossed 4000 times with the following table:

 Outcome HH HT TH TT Frequency 1100 950 1200 750
Explanation

Given Information:

The following table represents the frequency of outcomes when two distinguishable coins were tossed 4000 times and the uppermost faces are observed.

 Outcome HH HT TH TT Frequency 1100 950 1200 750

For a coin to be fair, the coin must have 50% chance for heads and tails to come up. This means that the relative frequency must be equal to 0.50.

To find the relative frequency, consider the provided table for the frequency of outcomes when two distinguishable coins were tossed 4000 times and the uppermost faces are observed,

 Outcome HH HT TH TT Frequency 1100 950 1200 750

When an experiment is performed N times, the relative frequency or estimated probability P(E) of an event E is the fraction of times fr(E) that the event E occurs.

It is given by, P(E)=fr(E)N

The relative frequency for the event ‘HH’ is calculated by substituting 1100 for fr(E) and 4000 for N,

P(HH)=fr(HH)N=11004000=1140=0.275

The relative frequency for the event ‘HT’ is calculated by substituting 950 for fr(E) and 4000 for N,

P(HT)=fr(HT)N=9504000=1980=0

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