akil Sprint 7:36 PM WHW 01.pdf PR 1 of 1 MP SCI SPRING 2018 First Last NetID See

Question

akil Sprint 7:36 PM WHW 01.pdf PR 1 of 1 MP SCI SPRING 2018 First Last NetID See the written assignment instructions, posted separotely. A king and his army will attempt to capture a fortress. The left and right flanks break off from the main group to attack the west and east guard towers. Suppose the left flank has a 60% chance of success and the right flank has a 75% chance of success, independently of one another. If both flanks capture their respective targets, then the king has a 98% chance of successfully taking the fort. lf, however, only the left flank captures its tower, the king has an 80% chance of success; if only the right flank succeeds, the king has a 50% chance. If both flanks fail, then the king's chance of capturing the fort drops to 20%. It turns out the king captures the fort. What is the probability that one, and only one, flank was successful (either the left, or the right, but not both)? Open With Print

Explanation / Answer

probability of both flank to be successful =0.6*0.75=0.45

probability that only left flank  to be successful =left flank to be successful-both flank successful =0.6-0.45=0.15

probability that onlyright flank  to be successful =right flank to be successful-both flank successful =0.75-0.45=0.30

probability that both failed =(1-0.6)*(1-0.75)=0.1

P(king captures the fort) =P(both flank succeed and captures)+P(only left flank succeed and captures)+P(only right flank succeed and captures)+P(both flank failed and captures)

=0.45*0.98+0.15*0.8+0.3*0.5+0.1*0.20=0.731

probability that only one flank was successful given captures the fort

=P(only left flank succeed and captures+only right flank succeed and captures)/P(captures)

=0.15*0.8+0.3*0.5/0.731=0.3252

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