7.5. Practice question answers

Chapter 7 practice question answers

7.1. Binomial Probability

1.  ≈ 0.0322

2.  a. 0.0064

     b. 0.2048

     c. 0.9424

3.  a. ≈ 0.1047

     b. ≈ 0.0604

     c. ≈ 0.0269

     d. ≈ 0.2026

4. a. ≈ 0.3650

    b. ≈ 0.2305

5. ≈ 0.6778

7.2. Bayes’ Formula

1.  a. 31/48

     b. 8/17

     c. 5/8

2.  a. 0.125

     b. ≈ 0.7241

3.  a. 0.045

     b. ≈ 0.2667

     c. 0.03

4.  a. 0.0572

     b. 0.07

     c. ≈ 0.0446

 

7.3. Expected Value and Tree Diagrams

1.  1.7

2.  ≈ -0.83 cents

3.  -0.96 cents

4.  ≈ -0.0519 cents

5.  0.94

6.  ≈ 0.5177

7.  0.776

8.  0.97

 

7.4. Markov Chains

1. 

    \begin{equation*} \mathbf{First\; Purchase\quad\quad} \begin{blockarray}{*{3}{c} l} \begin{block}{*{3}{>{$\footnotesize}c<{$}} l} & \BAmulticolumn{3}{c}{\textbf{Next Purchase}} & \\ & \quad Ford\quad\quad & \quad GM\quad\quad \\ \end{block} \begin{block}{>{$\footnotesize}l<{$}[*{3}{c}]} Ford & 0.60 & 0.40 \\ GM & 0.20 & 0.80 \\ \end{block} \end{blockarray} \end{equation*}

2.  a.  0.32

     b.  Shoot (S) = 2/3, Pass (P) = 1/3

3.  a.  31%

     b.  25%

4. a. 

    \begin{equation*} \mathbf{Before\quad\quad} \begin{blockarray}{*{3}{c} l} \begin{block}{*{3}{>{$\footnotesize}c<{$}} l} & \BAmulticolumn{3}{c}{\textbf{After}} & \\ & \quad Y\quad\quad & \quad N\quad\quad \\ \end{block} \begin{block}{>{$\footnotesize}l<{$}[*{3}{c}]} Reported accident (Y) & 0.25 & 0.75 \\ Didn't report accident (N) & 0.05 & 0.95 \\ \end{block} \end{blockarray} \end{equation*}

     b.  680

     c.  561

     d.  6.25%