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Numerade Educator

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Problem 72 Hard Difficulty

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 $\$ 50,000$ 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 $\$ 100,000 ?$

Answer

a) $P(\text { income }>\$ 50,000)=0.321$
b) $P( \geq \$ 100,000 | \geq \$ 50,000)=\frac{106}{321} \approx 0.3302$

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Video Transcript

all right. 72. We have you come and were given under 25 25 to 49. 50 to 99 100 for 99 and greater than or equal to 500. And our probabilities, our 0.431 for under 25 0.248 for 25 to 49. Wait to 15 or 50 to 99 0.1 for 104. 99.0 06 So, in part A, we're going to look at, um we're randomly selecting someone. No, we don't want to know the probability that they're making 50,000 or more. So I'm gonna add up my 0.215 plus 0.1 plus 0.6 in that equals 0.3 21 part B. Um, given they make over, find the probability given they make over 50,000 at based. What's that probability? They make at least 100,000. So my formula is at least 100,000 and at least 50,000. Well, that's just gonna be at least the hunt. Good 1000 which is gonna be 0.106 over the probability of at least 50,000 which is 0.3 21 No, when I divide that I get 0.3302