Chapter 5, Problem 1SE

Simulation (Example 1) If we flip a coin 10 times, what percentage of the time will the coin land on heads? A first step to answering this question is to simulate 10 flips. Use the random number table in Appendix A to simulate flipping a coin 10 times. Let the digits 0, 1, 2, 3, 4 represent heads and the digits 5, 6, 7, 8, 9 represent tales. Begin with the first digit in the fifth row.

a. Write the sequence of 10 random digits.

b. Change the sequence of 10 random digits to a sequence of heads and tails, writing H for the digits 0, 1, 2, 3, 4 and the T for the digits 5, 6, 7, 8, 9. What was the longest streak of heads in your list?

c. What percentage of the flips were heads?

To determine

Mention the sequence of 10 random digits from a random table.

Answer to Problem 1SE

The digits are 5, 5, 1, 8, 5, 7, 4, 8, 3, 4.

Explanation of Solution

The random number table is provided in Appendix A, and it is asked to choose 10 numbers starting from the first digit in the fifth row.

The first 10 digits in the fifth row are 5, 5, 1, 8, 5, 7, 4, 8, 3, 4.

To determine

Write the sequence of heads and tails using the 10 random digits, and determine the longest streak of heads in the list.

Answer to Problem 1SE

The required sequence is T, T, H, T, T, T, H, T, H, H. The longest streak of heads is 2 heads, at the end of the sequence.

Explanation of Solution

The 10 random digits that are taken from the table are 5, 5, 1, 8, 5, 7, 4, 8, 3, 4. Here, 0, 1, 2, 3, 4 represent heads, and 5, 6, 7, 8, 9 represent tails.

Consider H denotes heads, and T denotes tails. Now, the sequence of 10 random digits can be converted into heads and tails as given below.

$\begin{array}{|cccccccccc|}\hline 5& 5& 1& 8& 5& 7& 4& 8& 3& 4\\ \text{T}& \text{T}& \text{H}& \text{T}& \text{T}& \text{T}& \text{H}& \text{T}& \text{H}& \text{H}\\ \hline\end{array}$

It can be seen that the longest streak of heads is 2 heads, at the end of the sequence.

To determine

Find the percentage of heads.

Answer to Problem 1SE

The required percentage is 40 $\%$.

Explanation of Solution

The obtained sequence of heads and tails has 4 heads and 6 tails.

The percentage of flips that were heads can be calculated as,

$\begin{array}{c}\text{Percentage of heads}=\frac{\text{Number of heads}}{\text{Total number of flips}}\times 100\\ =\frac{4}{10}\times 100\\ =0.4\times 100\\ =40\%\end{array}$

Therefore, 40 $\%$ of flips resulted in heads.