Answer:
a)P=0.42
b) 
Step-by-step explanation:
We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:

a) we have k=2, n=10 and p=0.01:

b) We have,
, Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.

8 as you round up 405 to 400 and divide by 50 and get 8
I'll give you a hint
20) Add 56 to both sides
23) Add 1.5 to both sides
Also, as a AP Calc BC student, laziness doesn't really help get a good job soo...