Chapter 7.1, Problem 7.23E

To determine

To find: the design and carry out a simulation using random digits to help to decide who is correct.

Answer to Problem 7.23E

0.02

Explanation of Solution

Given:

Simulation of 250 flip of a coin and assuming that heads and tails are equally likely

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

10 possible digits are there so assigning 5 of the digits to heads and 5 of the digits to tails

Heads: Digit 0, 1, 2, 3, 4

Tails: Digit 5, 6, 7, 8, 9

Using the TI 83 calculator for simulating the result

Generating the 250 flips of a coin using the TI83/TI84 calculator

  $randInt\left(0,9,250\right)$

Counting the number of heads (digits 0, 1, 2, 3, 4) in the result and repeating the simulation 100 times in total

114, 123, 114, 136, 138 ...128

It is observed that the value 140 is mentioned twice in the last 100 values.

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{2}{100}\\ =0.02\end{array}$

Therefore the estimated probability is 0.02