Let Ai denote the event that a field goal is made by player i, i=1,2,3. Assume that A1,A2,A3 are mutually independent and that P(A1)= 0.5 P(A2)= 0.7 and P(A3)= 0.6.

Suppose that the probability of failure of a component isp= 0.4. Find the probability that the system does not fail if the number of redundant components is:

a.) 3

b.) 8