1. Simple Probability:
Compute these probabilities:
a. The probability of rolling the number 6 using one die.
b. The probability of rolling the number 6 twice in 2
rolls using only one die.
c. If the probability of seeing a male house finch at a
birdfeeder is .45 and the probability of seeing a
female house finch is .35; what is the probability of
seeing, first a male house finch, then a female house
finch, and finally another male house finch?
d. There are only 2 type of Pokemon: rare and
common. If the probability of finding a rare
Pokemon at a Pokestop is .05, what is the probability
that the first 8 Pokemon that you find are common,
and then you find one rare Pokemon at a Pokestop
that has a lure attached to it. Assume that you will
find at least 9 Pokemon in the 30 minutes that the
lure is attached.
2. Joint Probability:
An apple juice bottling company maintains records
concerning the number of unacceptable bottles of juice
obtained from the filling and capping machines. Based on
past data, the probability that a bottle came from machine I
and was nonconforming is 0.05 and the probability that a
bottle came from machine II and was nonconforming is
0.075. These probabilities represent the probability of one
bottle out of the total sample having the specified
characteristics. Half the bottles are filled on machine I and
the other half are filled on machine II.
a. If a filled bottle is selected at random, what is the
probability that it is a nonconforming bottle?
b. If a filled bottle is selected at random, what is the
probability that it was filled on machine II?
c. If a filled bottle is selected at random, what is the
probability that it was filled on machine I and is a
3. Lottery Probability:
Suppose that there is a lottery where you select 3
different numbers between 0 and 9. A digit cannot be
selected twice so you can select 123 but not 112.
a. How many different three digit numbers are possible?
b. If you buy one ticket, what is the likelihood you will
c. If you buy 3 tickets, what is the likelihood you will lose?
4. Probability using the z test:
According to Investment Digest ("Diversification and the
Risk/Reward Relationship", Winter 1994, 1-3), the mean of
the annual return for common stocks from 1926 to 1992
was 15.4%, and the standard deviation of the annual return
was 21.5%. During the same 67-year time span, the mean
of the annual return for long-term government bonds was
5.5%, and the standard deviation was 7.0%. The article
claims that the distributions of annual returns for both
common stocks and long-term government bonds are bell-
shaped and approximately symmetric. Assume that these
distributions are distributed as normal random variables with
the means and standard deviations given previously.
Here is a link to the z table:
a. What is the probability that the stock returns are
greater than 0%?
b. What is the probability that the stock returns are less