Answer Happy

A new structure is subjected to proof testing. Assume that the
maximum proof load is specified at a reasonably high level so that
the calculated probability of the structure surviving the maximum
proof load is 0.90. However, it is felt that this calculation is
only 70% reliable, and there is a 25% chance that the true
probability may be 0.50; moreover, there is even a 5% chance that
it may be only 0.10.
(a) What is the expected probability of survival before the
proof test?
(b) If only one structure is proof tested, and it survives the
maximum proof load, determine the updated distribution of the
survival probability.
(c) What is the expected probability of survival after the proof
test?
(d) If three structures were proof tested, and two of the
structures survived whereas one failed under the maximum proof
load, determine the updated expected probability of survival.