.
1. It is the same as the probability that all 8 are males.
P =
, or, which is the same,
P =
.
They are not only "different formulas" - they go with different explanations (=self-explanations),
but they produce identical results.
2. P =
.
3. P (at least 6 of the 8 are females) = P(0 males) + P(1 male) + P(2 males) =
+
+
.
4. P (at least 2 of the 8 are males) = complement to P(at most 1 of the 8 is male) = 1 - P(0 males) + P(1 male) = 1 -
-
.