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 $\backslash (50,000$ or more?

(b) Given that a return shows an income of at least $\backslash )50,000,$what is the conditional probability that the income is at least $\$100,000?$

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

For mutually exclusive events, use the following addition rule:

$P(AorB)=P\left(A\right)+P\left(B\right)$

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

Fill in the blanks with the corresponding probabilities:

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

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

$P(income>\$50000)=0.321$

$P(income>\$50000)=0.321$

$P(income\ge \$50000and\ge 100,000)=P(>100,000)$

condition probability: $P(A/B)=P(AandB)/P\left(B\right)$

$P(\ge \$100,000/\ge \$50,000)=\frac{P(\ge \$100,000and\ge \$50,000)}{P(\ge \$50,000)}$

$=\frac{0.106}{0.321}\approx 0.3302=33.2\%$

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

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