STAT101: Spring 2012
More Mideterm 2 Review Problems
Brian Powers TA
Here's a few more problems โ these may be a little more challenging but they will help prepare for the
exam.
1. If
P๎B๎=0.60
and
P๎AโฉB๎=0.10
, which is more likely: A|B or B|A?
2. If it rains there is a 70% chance that it is windy also. The forecast gives a 25% chance of rain.
Therefore, the probability of wind is
.70โ
.25=.175
(ie 17.5%) probability of wind.
What is wrong with this reasoning?
3. At a certain factory, units are produced on the assembly line one after the other. Sometimes there is a
glitch in the system and the factory produces defective items.
A defective item is produced after a working item with probability 0.1%. A defective item is followed
by another defective item with probability 95%. Assume that the machines are checked every night so
that the first item of the day is a working item with 100% probability.
โขWhat is the probability that the second item of the day is working?
โขWhat is the probability that the second through 5th items are all working?
โขWhat is the probability that the second item is defective by the 10 after it are all working?
โขWhat is the probability that the first 4 items of the day will be working, defective,
working, and working (in that order)?
โขIf item #3 is defective, what is the probability that item #2 was working?
โขIf the company produces 50 items today, what is the probability that the company will
only produce 1 defective item today?
โขIs the binomial distribution appropriate to predict the # of defective items produced? Why
or why not?
