A traveling salesman can be found at one of four cities (C1,C2,C3,C4) at any given time. His probability of being at these cities are P(C1) = 1/8, P(C2) = 1/8, P(C3) = 1/4, P(C4) = 1/2. He always carries his cellphone with him. Let X be the event that his cellphone has coverage. The conditional probabilities that his cell phone has coverage given what city he is at are as following: P(X|C1) = 1/2, P(X|C2) = 1, P(X|C3) = 3/4, P(X|C4) = 3/4. a. Given that today his cellphone has coverage, what is the probability that he is at city C2? b. Let Y be the event that his cellphone is at least 70% charged. He usually remembers to recharge his cell phone every evening so the probability that his cell phone is at least 70% charged at any given time is 4/5. Events X and Y are independent. What is the probability that his cellphone is less than 70% charged AND out of coverage at the same time?
A traveling salesman can be found at one of four cities (C1,C2,C3,C4) at any given time.
His probability of being at these cities are P(C1) = 1/8, P(C2) = 1/8, P(C3) = 1/4, P(C4) =
1/2. He always carries his cellphone with him. Let X be the
coverage. The conditional probabilities that his cell phone has coverage given what city he
is at are as following: P(X|C1) = 1/2, P(X|C2) = 1, P(X|C3) = 3/4, P(X|C4) = 3/4.
a. Given that today his cellphone has coverage, what is the probability that he is at city C2?
b. Let Y be the event that his cellphone is at least 70% charged. He usually remembers to
recharge his cell phone every evening so the probability that his cell phone is at least
70% charged at any given time is 4/5. Events X and Y are independent. What is the
probability that his cellphone is less than 70% charged AND out of coverage at the same
time?
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