Source: Official Guide Revised GRE 2nd Ed. Part 9; Section 5; #19

3

If one of the workers in the manufacturing

If one of the workers in the manufacturing and service industries who were unemployed for at least 1 week will be randomly selected, what is the probability that the person selected will be a service industry worker who was unemployed for 26 weeks or more? 0.04, 0.09, 0.21, 0.40, 0.90

2 Explanations

1

Lailya Leach

I'm not really understanding the solution. Do you mind explaining in a little more detail?

May 24, 2018 • Comment

David Recine

Sure thing, Laiya. :) Let's take a closer look at the shortcut Chris described in his video.

Chris is taking a very "number sense" approach to this video. What he's saying is that you can notice the following things about the data:

1) The total number of workers for the manufacturing industry pie chart is only a little bit more than the total number of workers in the service industry pie chart. (10 million vs. 8 million)

2) The percentage of workers who've been unemployed for 26+ weeks is also only slightly larger in manufacturing vs. service. (12% vs. 9%)

3) This means that, proportionally, we can roughly equate the number of workers who've been out of work for 26 weeks or more in both charts. We do this by imagining the charts are exactly equal-- imagining that the charts BOTH contain 8 million workers, instead of just one of the charts containing those, and imagining that the charts have 9% workers unemployed for 26 weeks or more.

4) From there, you can realize that if the charts were exactly equal, 9% of the workers being unemployed for more than 26 weeks on each chart would mean that for the total combined workers, 9% of all manufacturing and service workers would be unemployed for 26+ weeks.

5) This would also mean that the number of workers unemployed for 26+ weeks in the service industry would be half of the 26+ week group for all workers from both pie charts combined. That would be 4.5% of the workers. To convert this to a probability, convert 4.5% to the multiplier of 4.5%, which would be 0.045.

6) Realize that the real answer, adjusted for the real numbers in the first pie chart (10 million, 12%) would have to be relatively close to 0.045.

7) Realize that only (A), 0.04, is at all close in value to 0.045. the next closest option is (B) at 0.09. And that's really not close enough to be a possible answer.

I broke this down into very detailed steps, but the actual estimation is much faster than calculating out all the numbers.

You can check answer (A) by calculating out all the numbers if you want to, though.

In that case, the numbers would be:

(service workers unemployed 26+ months)/(all workers represented in the pie chart)

This comes out to:
(9% of 8 million)/(18 million)

Calculate that out fully, and you'll find you do indeed get 0.04, the same number you could estimate more rapid fire through steps 1-7 above. :)

5

Chris Lele

Dec 8, 2012 • Comment