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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

Part (a) P (income>$50000) = 0.321

Part (b) P (鈮 $100,000/ 鈮 $50, 000) = 33.2%

Step by step solution

01

Part (a) Step 1. Given Information

In the most recent year, the following is the distribution of adjusted go income reported on individual federal income tax returns:

02

Part (a) Step 2. Concept Used

For mutually exclusive events, use the following addition rule:

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

03

Part (a) Step 3. Calculation

For mutually exclusive events, use the addition rule: P(AorB)=P(A)+P(B)

Fill in the blanks with the corresponding probabilities:

P(income>$50000)=P(>50)

=P(5099)+P(100499)+P(500)=0.215+0.100+0.006=0.321

As a result, the likelihood of a random selection returning is

P(income>$50000)=0.321

04

Part (b) Step 3. Calculation

P(income>$50000)=0.321

P(income$50000and100,000)=P(>100,000)

=0.100+0.006=0.106

condition probability: P(A/B)=P(AandB)/P(B)

P($100,000/$50,000)=P($100,000and$50,000)P($50,000)

=0.1060.3210.3302=33.2%

As a result, the conditional probability of earning at least $100,000 is

P($100,000/$50,000)=33.2%

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