Doubt in this probability problem (Choosing Smart Numbers)

why d is not correct option?(a is correct one)

my logic:
(1-p) is the probability of x not happening when Y happens. so for 5 times, it should be (1-p)^5

Hint: what does “X does not happen at least once” mean? It’s a bit of a tongue-twister.

“X does not happen at least once” means that X can happen 0,1,2,3,4 times but not all the 5 times, right?
so we will subtract the probability of the case when X happens in all times, i.e.: p^5
the answer will be : 1-p^5

right?

Indeed.

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