Question: I am confused. If peanut proteins are in vaccines then why didn't my daughter have a reaction when she got her vaccines last week?

Let me explain it using marbles. We are going to make a big batch of vaccine, enough for 100 shots. (This is totally fictitious and the numbers and protein does not coincide with actual vaccines.)

The trace amount of protein is represented by the following marbles:

Protein from the mixed oils in the diluent in the adjuvant:

Peanut protein  - 16 marbles

Soy protein - 4 marbles

Lupin protein - 2 marbles

Sesame protein - 3 marbles

Protein from the culture medium:

Beef protein - 2 marbles

Total marbles in the batch of vaccine: 27 marbles

It is possible for one shot to have all 27 marbles in it. Or one marble could be in only one shot - so 27 of the shots have one marble each.

So the chances of there being a shot with no protein in it is at least (100 - 27) = 73 out of 100

And your daughter would have had to get one of the shots with peanut protein in it to have a reaction which is only 16/100 or 16% chance.