Once you know how many pages each printer handles, use the jam percentages to find how many of those pages jam for X, Y, and Z separately.

You are choosing from the set of jammed pages only. Among those jammed pages, what fraction came from printer Z?

Place the number of jammed pages from Z over the total number of jammed pages from all printers, then simplify the fraction.

In the Desmos expression line, type the exact probability expression using decimals: (0.25*0.05) / (0.40*0.02 + 0.35*0.03 + 0.25*0.05). The numeric result that Desmos shows is the probability that a jammed page came from Z; you can then match this decimal to the closest fraction in the answer choices.

The question asks: given that a page jammed, what is the probability it was printed by Z?

In probability notation, that is $P(\text{Z} \mid \text{jam})$. To find this, you can think:

So we need the number of jammed pages from each printer.

To make the percentages easy to work with, assume the company printed 10,000 pages in total (any large round number works, like 100 or 1,000; the ratio will be the same).

Using the first column of the table:

• Printer X prints $40\%$ of 10,000 pages: $0.40 \times 10{,}000 = 4{,}000$ pages.
• Printer Y prints $35\%$ of 10,000 pages: $0.35 \times 10{,}000 = 3{,}500$ pages.
• Printer Z prints $25\%$ of 10,000 pages: $0.25 \times 10{,}000 = 2{,}500$ pages.

Now use the second column (jam percentages for each printer):

• X: $2\%$ of X's 4,000 pages jam:
  $0.02 \times 4{,}000 = 80$ jammed pages from X.
• Y: $3\%$ of Y's 3,500 pages jam:
  $0.03 \times 3{,}500 = 105$ jammed pages from Y.
• Z: $5\%$ of Z's 2,500 pages jam:
  $0.05 \times 2{,}500 = 125$ jammed pages from Z.

Total jammed pages from all printers:

We want the probability that a randomly chosen jammed page came from Z:

Now simplify $\dfrac{125}{310}$ by dividing top and bottom by 5:

So the correct answer is $\dfrac{25}{62}$.