distribution of adjust gross income in individual federal income tax returns shows:

Income: 30-74, 75-199, more than 200
Probability: 0.315, 0.180, 0.031

1. What is the probability that a randomly chosen return shows an adjusted gross income of $30,000 or more?

2. Given that a return shows an income of at least $30,000, what is the conditional probability that the income is at lest $75,000?

If it is 30,00 or more.. I think you would just add all of the probabilities.

.315+.180+.031

huj

To answer these questions, we can use the given probability distribution. Here's how you can find the probabilities step by step:

1. To find the probability that a randomly chosen return shows an adjusted gross income of $30,000 or more, we need to find the sum of the probabilities for incomes of $30,000 or more.

- In this case, we have income ranges of 30-74, 75-199, and more than 200.
- The probability of income being $30,000 or more is the sum of the probabilities for the second and third income ranges.
- So, the probability is 0.180 + 0.031 = 0.211.
- Therefore, the probability that a randomly chosen return shows an adjusted gross income of $30,000 or more is 0.211, or 21.1%.

2. To find the conditional probability that the income is at least $75,000 given that the return shows an income of at least $30,000, we need to calculate the ratio of the probability of incomes at least $75,000 to the probability of incomes at least $30,000.

- We already know the probability of incomes at least $30,000 is 0.211.
- Now, we need to find the probability of incomes at least $75,000.
- From the given distribution, we see that the probability of income being at least $75,000 is 0.180 + 0.031 = 0.211, which is the same as the probability of incomes at least $30,000.
- Therefore, the conditional probability that the income is at least $75,000 given that the return shows an income of at least $30,000 is 0.211 or 21.1%.