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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: 鈥淲ho usually prepares your tax return?鈥� 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, 鈥淭he Impact of Multiple Tax Returns on Tax Compliance Behavior,鈥� 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

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

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

Hence, the required probability is 0.54.

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