How much larger a share of the breakthrough cases in Israel do people 50 and older represent?

Question

In Israel, People 50 and older are 26% of the population. They account for 40% of breakthrough COVID cases (5158 in total). People under 50 are 74% of the population. They account for 60^ of breakthrough COVID cases (7737 in total).

Question: How much more likely are people 50 and older to get breakthrough infections than people under fo? How much larger a share of the breakthrough cases in Israel do people 50 and older represent?

Answer 1

Total COVID cases=5158+7737=12895. Ratio 7737:5158=60:40=3:2.

To compare the COVID cases for the two groups, it's necessary to adjust the figures so that they rest on the same base. One way to do this is to boost the figures to the common base of 100%. Then the breakthrough cases can be compared directly.

If 26% is equivalent to 5158 cases, then 100% is equivalent to (100/26)5158=19838.46 cases approx.

If 74% is equivalent to 7737 cases, then 100% is equivalent to (100/74)7737=10455.41 cases approx.

Now we can compare these two figures: 19838.46/10455.41=⅔×(74/26)=74/39=1.90 approx. This represents a ratio:

(over 50s):(under 50s)=19:10 approx.

This means that the over 50s are about 90% more likely than under 50s to get breakthrough infections.

In terms of shares we have 1.90/2.90=0.6549 approx, or over 50s have about 65.5% of the share of breakthrough infections.