Answer:
Probability is 0.831727
Step-by-step explanation:
The probability can be calculated as below
There are multiple scenarios
Scanerio 1
0 occurance & No damage = 1 - 0.2 - 0.03 - 0.001 = 0.769
Scanerio 2
1 occurance & No damage = 0.2 x ( 1 - 0.7 ) = 0.06
Scanerio 3
2 occurance & No damage = 0.03 x ( 1 - 0.7 )^2 = 0.0027
Scanerio 4
3 occurance & No damage = 0.001 x ( 1 - 0.7 )^3 = 0.000027
P(structure will not suffer any damage) = Scanerio 1 + Scanerio 2 + Scanerio 3 + Scanerio 4 = 0.769 + 0.06 + 0.0027 + 0.000027 = 0.831727
To split this trinomial into two binomials, let's try and find two numbers which add to 6 and multiply to 8. To do this, we can list all the factors of 8 and then choose which factors also add to 6.
Factors of 8: (1, 8), (2, 4)
1 + 8 = 9, meaning that 1 and 8 are not the factors we are looking for. However, 2 and 4 do add to 6. By combining these numbers which an x (so that we can produce the
term at the front of the trinomial), we find the binomials:
and 
The answer is x + 2 and x + 4.