I don’t think these probabilities are correct. Every parent is told not to feed their under 1 year olds honey, many times.
In an extreme example… only 20 parents fed their kids honey and 20 kids contracted botulism.
That would be a 100% risk. Obviously in real life it’s not 100% of kids, but still could be a meaningful percentage and likely higher than 1 in 50,000 for babies that eat honey.
It is correct. They are considering the most extreme case; in the most extreme case, no non-botulism-infected infants eat honey, and honey was the cause of botulism for those 20 infants.
If that is so, then completely removing honey exposure for infants would mean that 80 rather than 100 infants get botulism poisoning.
So the new probability of contracting botulism is (80 / 100) * (old probability), and (80 / 100) * (1 / 40000) = 1 / 50000.
There are no errors in the calculation, but it's wrong anyways because it calculates the answer to the wrong question. "At best" suggests this is the largest possible effect, but it is the smallest possible. To get an upper bound estimate on the usefulness of avoiding honey, you would need to know how many parents of 1-year-olds are avoiding honey.
Yeah, and their infant mortality is on par with Sub-Saharan Africa.
"The second most common prelacteal feed is honey, a delicious natural sweetener. Numerous studies [29,30] have shown that the ingestion of honey under one year of age is linked with infant botulism, a disease that results in a blockade of voluntary motor and autonomic functions. Apart from this, other prelacteal feeds get contaminated due to unhygienic environment, especially in rural India and in urban slums, resulting in infantile diarrhea. Thus, a wide range of prelacteal feeds and the introduction of early supplements result in recurrent diarrhea with multiple illness finally ending lives because of inaccessibility and unaffordibility of treatment and delayed or inappropriate care seeking behavior."
The paper lists a bunch of other traditional practices that have deleterious effects on the infants' health, such as putting unsanitary herbal concoctions on the babies navel while it's still healing, etc.
"Diarrhoea is a leading killer of children, accounting for approximately 9 per cent of all deaths among children under age 5 worldwide in 2021. This translates to over 1,200 young children dying each day" - https://data.unicef.org/topic/child-health/diarrhoeal-diseas...
"OK, sister bees, now remember: this season we'll be feeding the hu-man's child, so wipe your feet before entering the hive, and if you feel the sniffles coming on, Don't Make Honey!"
It's more about the below minimum wage people harvesting, bottling for transport, transporting, then bottling for sale than the bees themselves. More intermediate steps to introduce contamination and more potentially contaminated sources all mixed together.
In an extreme example… only 20 parents fed their kids honey and 20 kids contracted botulism.
That would be a 100% risk. Obviously in real life it’s not 100% of kids, but still could be a meaningful percentage and likely higher than 1 in 50,000 for babies that eat honey.