Say I use a toaster every work week and there is a 20% chance of me getting shocked by using it, then what is the probability of getting shocked just once a work week?
The answer is 41% using the binomial formula but I’m confused...
My reasoning -
The probability of getting shocked on a given day but not on the other days = 0.2 * 0.8 * 0.8 * 0.8 * 0.8 = ~8.2%.
Shouldn’t this be the answer instead of 8.2%*5?
You don't state it explicitly, but from the context it seems the $20\%$ chance of being shocked is for within any given day. If so, then what you've shown is the probability of being shocked on only one particular day, say Monday, during a $5$ day work week is $\approx 8.2\%$. However, to be shocked exactly once during a work week means you can be shocked on just one of any of the $5$ work days in a week. As such, you need to add the probabilities of being shocked on that just one day, but not the other days, for all of the $5$ work days, to get (note I'm using your approximation of $8.2\%$ although the correct value is actually $8.192\%$)
$$8.2\% + 8.2\% + 8.2\% + 8.2\% + 8.2\% \approx 5(8.2\%) = 41\% \tag{1}\label{eq1A}$$