Tossing three coins doesn't increase the odds of any one of them being heads, surely enough. But tossing them at the same time as a single combined trial, instead of just one coin, does increase the odds of at least one heads showing up from 50 to 87.5%.
Of course, you're going to have all those vaccines anyway and so the odds are the same overall for those administrations. Just like it doesn't matter whether we toss three coins at the same time, or weeks apart; the odds are 87.5% we will see a head.
But grandparent has a point about a situation like getting multiple vaccines before travel, where you're making it more likely that side effect will occur during that specific inconvenient time.
Tossing three coins doesn't increase the odds of any one of them being heads, surely enough. But tossing them at the same time as a single combined trial, instead of just one coin, does increase the odds of at least one heads showing up from 50 to 87.5%.
Of course, you're going to have all those vaccines anyway and so the odds are the same overall for those administrations. Just like it doesn't matter whether we toss three coins at the same time, or weeks apart; the odds are 87.5% we will see a head.
But grandparent has a point about a situation like getting multiple vaccines before travel, where you're making it more likely that side effect will occur during that specific inconvenient time.