Step-by-step explanation:
the probability of 1 tested insect is killed is 60% or 0.6.
the probability that it is not killed is then 1-0.6 = 0.4.
when we test 7 insects and exactly 4 survive is the event that
3 insects are killed, 4 insects survive.
the probability for one such case is
0.6×0.6×0.6 × 0.4×0.4×0.4×0.4
how many such cases do we have ?
as many as ways we can select 4 insects out of the given 7.
these are 7 over 4 combinations :
7! / (4! × (7-4)!) = 7! / (4! × 3!) = 7×6×5/(3×2) = 7×5 = 35
so, the probability that exactly 4 out of 7 tested insects survive is
35 × 0.6³ × 0.4⁴ = 0.193536 ≈ 0.1935
