PROBABILITYFred is working on a major project. In planning the project, two milestones are set up,
with dates by which they should be accomplished. This serves as a way to track Fred’s
progress. Let $A_1$ be the event that Fred completes the first milestone on time, $A_2$ be
the event that he completes the second milestone on time, and $A_3$ be the event that he
completes the project on time.
Suppose that $P(A_{j+1}|A_j) = 0.8$ but $P(A_{j+1}|{A_j}^c
) = 0.3$ for $j = 1, 2$, since if Fred falls
behind on his schedule it will be hard for him to get caught up. Also, assume that the
second milestone supersedes the first, in the sense that once we know whether he is
on time in completing the second milestone, it no longer matters what happened with
the first milestone. We can express this by saying that $A_1$ and $A_3$ are conditionally
independent given $A_2$ and they’re also conditionally independent given ${A_2}^c$.
(a) Find the probability that Fred will finish the project on time, given that he completes
the first milestone on time. Also find the probability that Fred will finish the project on
time, given that he is late for the first milestone.
(b) Suppose that $P(A_1) = 0.75$. Find the probability that Fred will finish the project
on time. 15th EditionDouglas A. Lind, Samuel A. Wathen, William G. Marchal1,236 solutions

5th EditionDaniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor2,433 solutions

4th EditionChris Olsen, Jay L. Devore, Roxy Peck552 solutions

1st EditionDavid R. Anderson, James J Cochran, Jeffrey D. Camm, Jeffrey W Ohlmann, Michael J Fry441 solutions