Who prepares your tax return? As part of a study on income tax compliance (Behavioral Research and Accounting, January 2015), researchers sampled 270 adults at a shopping mall and asked each: “Who usually prepares your tax return?” Their answers (and frequency of responses) are shown in the table (p. 170). Use the information in the table to estimate the probability that a randomly selected adult uses a friend, relative, or professional to prepare his or her income tax return.

Table for Exercise 3.16

Response	Frequency
You	100
Your spouse	16
Equally with spouse	7
Friend or relative	31
Professional help	114
Not required to file	2
TOTAL	270

Source: S. Bhattacharjee, K. Moreno, and D. Salbador, “The Impact of Multiple Tax Returns on Tax Compliance Behavior,” Behavioral Research and Accounting, Vol. 27, No. 1, January 2015 (from Table 1).

Step by step solution

01

Step-by-Step SolutionStep 1: Introduction

Probability measures the likelihood of an event occurring in a Random experiment. The probability formula is used to determine the probability of an event occurring. The formula for determining the likelihood of an event is as follows:

$\mathbf{Probability}\mathbf{=}\frac{\mathbf{Favourable}\mathbf{}\mathbf{outcome}}{\mathbf{Total}\mathbf{}\mathbf{outcome}}$

02

Find the probability of a friend, relative, or professional

$\begin{array}{l}\mathbf{Total}\mathbf{}\mathbf{of}\mathbf{}\mathbf{friends}\mathbf{,}\mathbf{relatives}\mathbf{}\mathbf{or}\mathbf{}\mathbf{professional}\mathbf{=}\mathbf{31}\mathbf{+}\mathbf{114}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{145}\end{array}$

$\begin{array}{l}\mathbf{P}\mathbf{\left(}\mathbf{atleast}\mathbf{20}\mathbf{yearsofexperience}\mathbf{\right)}\mathbf{=}\frac{\mathbf{145}}{\mathbf{270}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{54}\end{array}$

Hence, the required probability is 0.54.

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