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# Bayes theorem / conditional probability help watch

1. In Scotland the household incomes of the population is 50% of the households are considered low income, 40% are considered moderate income, and 10%
are considered high income. The probability that a low income household will
evade tax is 0.1. The corresponding probabilities for moderate income and high income households are
0.2 and 0.6 , respectively.

1. What is the probability that a randomly chosen household is a low income tax evader
2. What proportion of tax evaders have a low income?

I have set P(L) = 0.50, P(M) = 0.40, P(H) = 0.10 along with P(T|L) = 0.10, P(T|M) = 0.20 and P(T|H) = 0.6

For part 1) are they asking for P(LnT) or are they literally asking me to regurgiate information provided within the text?

Also for part 2.) would it be the same as doing P(LnT) / P(t) * 100 ?
2. (Original post by TwiMaster)
In Scotland the household incomes of the population is 50% of the households are considered low income, 40% are considered moderate income, and 10%
are considered high income. The probability that a low income household will
evade tax is 0.1. The corresponding probabilities for moderate income and high income households are
0.2 and 0.6 , respectively.

1. What is the probability that a randomly chosen household is a low income tax evader
2. What proportion of tax evaders have a low income?

I have set P(L) = 0.50, P(M) = 0.40, P(H) = 0.10 along with P(T|L) = 0.10, P(T|M) = 0.20 and P(T|H) = 0.6

For part 1) are they asking for P(LnT) or are they literally asking me to regurgiate information provided within the text?

Also for part 2.) would it be the same as doing P(LnT) / P(t) * 100 ?
For part 1) I also think it is P(LnT).

For part 2) think about how you can use Bayes' Theorem and what you need to find out. The denominator should end up being P(T) by law of total probablity and your numerator needs to be rewritten but otherwise should be correct.
3. (Original post by SeanFM)
For part 1) I also think it is P(LnT).

For part 2) think about how you can use Bayes' Theorem and what you need to find out. The denominator should end up being P(T) by law of total probablity and your numerator needs to be rewritten but otherwise should be correct.
Hmm, how should the numerator be rewritten?
4. (Original post by TwiMaster)
Hmm, how should the numerator be rewritten?
Well, what is part 2 asking you to find? P(.... given ....). So using Bayes' Theorem..

Though thinking about it your numerator is fine, it's just not clear how you got there.
5. (Original post by SeanFM)
Well, what is part 2 asking you to find? P(.... given ....). So using Bayes' Theorem..
P(T|L) im assuming
6. (Original post by TwiMaster)
P(T|L) im assuming
Other way round

But I think your numerator is fine, you just didn't show your steps to getting to that equation.

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Updated: November 7, 2015
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