1.
Suppose
E is an event in a sample space S with probability .3. What is the probability
of the complement of E?
2.
Suppose
E and F are events in a sample space S. Suppose further that E has probability
.5, F has probability .6, and the intersection of E and F has probability .2.
Find the probability of the union of E and (the complement of F)
3.
Two
six-sided dice are rolled. Find the probability that the sum is 8 given that
the first die was 3.
4.
Two
six-sided dice are rolled. But this time, the dice aren't fair: For each die, a
1 is twice as likely to be rolled as a 2, a 2 is twice as likely to be rolled
as a 3, ..., and a 5 is twice as likely to be rolled as a 6 (in other words,
each number is twice as likely as the number that follows it). So what is the
probability of rolling a sum of 7?
5.
We're
playing poker with a standard pack of fifty-two cards without jokers. You have
two pairs: 3, 3, 4, 4, 8. You are unaware of which cards the other players are
holding. You decide to replace the 8 by another card from the pack. How do you
rate your chances to turn your hand into a full house? (Full house means one
trio and one pair.)
6.
Eight
cardboard boxes are standing on the table. Two among them contain a present,
the other six are empty. You are allowed to open two boxes. How much chance do
you have to find at least one present?
7.
A
game show requires you to randomly pick 1 of 6 envelopes. The host has hidden a
$100 bill in one envelope, and a $1 bill in each of the other 5. Once you've
picked, the host is required to remove 2 $1 envelopes you didn't pick. You now
have a choice of keeping your original envelope, or paying $2 to switch your
choice to one of the 3 you didn't pick.
If you choose to pay $2 and switch your choice, then what are your odds of
losing money?
8.
A study has been done to determine whether or
not a certain drug leads to an improvement in symptoms for patients
with a particular medical condition. The results are shown in the
following table.ImprovementNo ImprovementTotalDrug270530800No Drug120280400Total3908101200Based
on this table, what is the (empirical) probability that a patient shows
improvement if it is known that the patient was given the drug?
A.
None of the answers given
B.
C.
D.
9.
The results of the study in question #9 on the
relationship between a certain drug and the improvement in symptoms for
patients with a particular medical conditon are repeated below. ImprovementNo ImprovementTotalDrug270530800No Drug120280400Total3908101200Based on this table, are the events "has the drug" and "improvement" independent events?
A.
No, they are not independent
B.
Yes, they are independent
10.
A company has three plants at which it produces a certain item. 30% are
produced at Plant A, 50% at Plant B, and 20% at Plant C. Suppose that
1%, 4% and 3% of the items produced at Plants A, B and C respectively
are defective. If an item is selected at random from all those
produced, what is the probability that the item was produced at Plant B
and is defective?
A.
B.
None of the answers given
C.
D.
11.
In a group of 339 people, at least two of them have the same first-name
and last-name initials, possibly switched (as in Constance Smith and
Selwyn Crown)