Like. I know they are different and that one is less likely. But could someone explain this in a way that I can explain it to my partner? I know it is true but cannot remember anything about why and how to explain my point.
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Everyone commenting so far has missed that their expected values are, in fact, identical. 1 x 0.7 = 10 x (0.07) = EV in both cases.
It depends on what OP means by “less likely”…less likely to do what, to “win” at least once? In that case, yes the (P>=1)s are indeed different as the first case is 70%, and the latter is 51.6% per the binomial distribution.
In a naive way, one can think of it as “both have the same mathematical expected value. However in return for the possibility of winning > once, multiple trials decrease the odds of winning at least once.”
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