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:

Income: <25 25–49 50–99 100–499 $500 Probability: 0.431 0.248 0.215 0.100 0.006

(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?