The phrase “selected from pages that jammed” signals conditional probability: the page is already known to have jammed. All jammed pages, not all printed pages, form the denominator. On a 100-page scale, use Desmos to find each printer’s contribution to the jams, then compare Z’s contribution with their total. Don’t divide by the overall share of pages printed by Z.
Hints
- Hint 1
A condition limits which pages could be selected. Since the chosen page jammed, the denominator must include jammed pages from X, Y, and Z, but no pages that printed without a jam.
- Hint 2
Each printer’s jam percentage applies to pages from that printer. On a scale of 100 total pages, use the first percentage column to find each printer’s portion before applying its jam rate.
- Hint 3
Add the jam contributions from all three printers before dividing. Z’s contribution is the numerator, but X and Y can also produce pages in the jammed-page group.
Step-by-step
Compare jam contributions
Step 1Choose the group being sampled
The page is selected from those that jammed. That is the condition, the fact already known about the page. So
The symbol means “given that.” The denominator is all jammed pages, not all printed pages.
- Step 2
Find each printer’s jam contribution
Use a scale of 100 total printed pages. The first column gives X, Y, and Z portions of , , and pages per 100. Each jam rate applies only to its own portion. Type in Desmos. It shows : these are the jam contributions per 100 printed pages, in X, Y, Z order. Don’t apply Z’s to all 100 pages.
- Step 3
Find the total jam contribution
X, Y, and Z account for all print jobs, so add all three entries. Type ; Desmos shows . That is the total jam contribution per 100 printed pages, and it supplies the denominator.
- Step 4
Compare Z’s jams with all jams
Z is the third entry of , so type . Desmos shows about ; its fraction button gives . So the probability that a randomly selected jammed page came from printer Z is . Choice D.