ST361 HW3 (due Thursday, 9/19/13)
(a) Show your work in order to earn the full credit. This means that you have to
present your steps or explain your reasoning for the answers you obtain, rather
than just to write down the answer itself.
Note that answers without steps or reasoning will receive 0 credits even if the
answers are correct!
(b) Remember to staple your homework and write your name on your
homework.
1) 5.16 (p.210) (Note that “mutually exclusive” means “disjoint”.)
2) 5.19 (p.210) (Hint for (b): If events A and B are independent, then so are the pairs of
events A’ and B, A and B’, and A’ and B’)
3) 5.20 (p.210~211) (Hint: we covered a similar example (pages 9-10 of handout ch5.3) in
class)
4) (Hint: we covered a similar example (page 7) in class)
At a certain gas station, 40% of the customers use regular unleaded gas, 35% use
extra unleaded gas, and 25% premium unleaded gas. It is also known that of the
customers using regular gas, only 30% will fill their tank; of the customers using extra
gas, 60% will fill their tanks; of the customers using premium, 50% will fill their tanks.
We want to use these data to predict the behavior of the next customer.
(a) What is the probability that the next customer will request extra unleaded gas and
fill the tank?
(b) Assume the probability that the next customer fills the tank is 0.455. If the next
customer fills the tank, what is the probability that extra gas is required?
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