Four students must work together on a group project. They decide that each
will take responsibility for a particular part of the project, as follows:
Because of the way the tasks have been divided, one student must finish before
the next student can begin work. To ensure that the project is completed on
time, a time line is established, with a deadline for each team member. If any
one of the team members is late, the timely completion of the project is
jeopardized. Assume the following probabilities:
1\. The probability that Maria completes her part on time is 0.8
2\. If Maria completes her part on time, the probability that Alex completes
on time is \(0.9,\) but if Maria is late, the probability that Alex completes on
time is only 0.6 .
3\. If Alex completes his part on time, the probability that Juan completes on
time is \(0.8,\) but if \(\mathrm{Alex}\) is late, the probability that Juan
completes on time is only 0.5 .
4\. If Juan completes his part on time, the probability that Jacob completes
on time is \(0.9,\) but if Juan is late, the probability that Jacob completes on
time is only 0.7 . Use simulation (with at least 20 trials) to estimate the
probability that the project is completed on time. Think carefully about this
one. For example, you might use a random digit to represent each part of the
project (four in all). For the first digit (Maria's part), \(1-8\) could
represent on time, and 9 and 0 could represent late. Depending on what
happened with Maria (late or on time), you would then look at the digit
representing Alex's part. If Maria was on time, \(1-9\) would represent on time
for Alex, but if Maria was late, only \(1-6\) would represent on time. The parts
for Juan and Jacob could be handled similarly.
