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Problem 10

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. $$ \begin{array}{|r|c|c|c|c|} \hline \text { Outcome } & \text { HH } & \text { HT } & \text { TH } & \text { TT } \\ \hline \text { Frequency } & 1,100 & 950 & 1,200 & 750 \\ \hline \end{array} $$ What is the relative frequency that the first coin lands with heads up?

Expert verified

The relative frequency of the first coin landing heads up is 0.5125 or 51.25%.

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Chapter 7

Complete the following. The relative frequency of an event \(E\) is defined to be __________

Chapter 7

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the given pair of events for independence. If a coin is tossed 11 times, find the probability of the sequence $\mathrm{H}, \mathrm{T}, \mathrm{T}, \mathrm{H}, \mathrm{H}, \mathrm{H}, \mathrm{T}, \mathrm{H}, \mathrm{H}, \mathrm{T}, \mathrm{T}$.

Chapter 7

Publishing Exercises \(37-46\) are based on the following table, which shows the results of a survey of 100 authors by \(a\) (fictitious) publishing company: $$ \begin{array}{r|c|c|c} & \begin{array}{c} \text { New } \\ \text { Authors } \end{array} & \begin{array}{c} \text { Established } \\ \text { Authors } \end{array} & \text { Total } \\ \hline \text { Successful } & 5 & 25 & 30 \\ \hline \text { Unsuccessful } & 15 & 55 & 70 \\ \hline \text { Total } & 20 & 80 & 100 \\ \hline \end{array} $$Compute the relative frequencies of the given events if \(a n\) author as specified is chosen at random. An author is unsuccessful.

Chapter 7

Explain how the property \(P\left(A^{\prime}\right)=1-P(A)\) follows directly from the properties of a probability distribution.

Chapter 7

How can the modeled probability of winning the lottery be nonzero if you have never won it despite having played 600 times? [HINT: See the definition of a probability model.]

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