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Chapter 5: Q 66. (page 332)

Income tax returns Here is the distribution of the adjusted gross income (in thousands of dollars) reported on individual federal income tax returns in a recent year:

a. What is the probability that a randomly chosen return shows an adjusted gross income of \(50,000 or more?

b. Given that a return shows an income of at least \)50,000, what is the conditional

probability that the income is at least $100,000?

Short Answer

Expert verified

a. Probability shows an adjusted gross income of $50,000or more is 0.321

b. Required conditional probability is0.3302

Step by step solution

01

Given Information

It is given that

02

Determining Probability for the randomly chosen return shows an adjusted gross income of $ 50,000 or more. 

As per addition rule

P(AorB)=P(A)+P(B)

From table, probability of adjusted gross income of 50-99(in thousands of$)

P(50-99)=0.215

Similarly P(100-499)=0.100

P(鈮�500)=0.006

Now, P(income>$50,000)=P(>50)

=P(50-99)+P(100-499)+P(鈮�500)

=0.215+0.100+0.006

=0.321

Hence, Probability shows an adjusted gross income of$50,000or more is0.321

03

Conditional Probability for income is at least $100,000

We know that P(A鈭�B)=P(AandB)P(B)

From above part: P(income>$50,000)=0.321

As return shows income of atleast $50,000

鈬�P(鈮�$50,000and鈮�$100,000)=P(鈮�$100,000)

=P(100-499)+P(鈮�500)

=0.100+0.006

=0.106

Using Conditional Probability

P(鈮�$100,000鈭�鈮�$50,000)=P(鈮�$50,000and鈮�$1,00,000)P(鈮�$50,000)

=0.1060.321

鈮�0.3302

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