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Alik [6]
3 years ago
6

What are the tax liability, the marginal tax rate, and the average tax rate for a married couple filing jointly with $51,900 tax

able income?
Business
1 answer:
Pachacha [2.7K]3 years ago
5 0

Answer:

Tax Liability: $5,840

Marginal Tax Rate: 12%

Average Tax Rate: 11%

Explanation:

*The tax liability is determined using the tax rate for 2019 tax bracket.

For married couple filling jointly, the tax rates for taxable income of $51,900 are:

Tax Rate                  Income Bracket

10%                          $0 – $19,400

12%                           $19,401 – $78,950

So the tax liability will be:

10% * $19,400 = $1,940                            (first $19,400)

12% * $32,500 = $3,900                           (Balance of $32,500)

Total tax liability = $5,840.

*Marginal tax rate is the tax rate paid on the last unit of income, the last dollar.  In this case, the last dollar was taxed at 12%. Hence the marginal tax rate is 12%.

*Average tax rate is the proportion of taxable income that is to be paid as tax. It is derived by dividing the tax liability by taxable income.

Average tax rate =<u> $5840</u>

                               $51,900

Average tax rate =11.2524%

Average tax rate = 11% (rounded up to whole figure)

         

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Answer:

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b) Probability of cancer given a negative test is P(C|-) = 0.0161

c) Probability of prostrate cancer given a positive test is P(C|+) = 0.3137

d) Probability of cancer given a negative test is P(C|-) = 0.2553

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According to Baye's theorem, P(C|+) = P(+|C)P(C)/P(+)

For P(+), we use the Law Of Total Probability: P(+) = P(+|C)P(C) + P(+|C')P(C')

P(+) = (0.8 * 0.02) + (0.75 * 0.98) = 0.751

Therefore, P(C|+) = P(+|C)P(C)/P(+)

P(C|+) = (0.8 * 0.02)/0.751 = 0.0213

b) Probability of cancer given a negative test is P(C|-)

According to Baye's theorem, P(C|-) = P(-|C)P(C)/P(-)

P(-) = P(-|C)P(C) + P(-|C')P(C')

P(-) = (0.2 * 0.02) + (0.25 * 0.98) = 0.249

Therefore, P(C|-) = (0.2 * 0.02)/0.249

P(C|-) = 0.0161

Part 2: Given the following;

Probability male patient has prostate cancer, P(C) = 0.3

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P(negative test given there is cancer) = P(false negative) = P(-|C) = 0.2

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Probability of positive test given there is prostrate cancer, P(+|C) is the complement of P(-|C), = 1 - 0.2 = 0.8.

c) Probability of prostrate cancer given a positive test is P(C|+)

According to Baye's theorem, P(C|+) = P(+|C)P(C)/P(+)

For P(+), we use the Law Of Total Probability: P(+) = P(+|C)P(C) + P(+|C')P(C')

P(+) = (0.8 * 0.3) + (0.75 * 0.7) = 0.751

Therefore, P(C|+) = P(+|C)P(C)/P(+)

P(C|+) = (0.8 * 0.3)/0.765 = 0.3137

d) Probability of cancer given a negative test is P(C|-)

According to Baye's theorem, P(C|-) = P(-|C)P(C)/P(-)

P(-) = P(-|C)P(C) + P(-|C')P(C')

P(-) = (0.2 * 0.3) + (0.25 * 0.7) = 0.235

Therefore, P(C|-) = (0.2 * 0.3)/0.235

P(C|-) = 0.2553

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