A.P. Statistics Review on Unit 4 ‘Probability’
Lefties Assume 13% of people are left-handed.
I. If we select 5 people at random, find the probability of each outcome described
below:
a. The first lefty is the first person chosen.
b. There are some lefties among the 5 people.
c. The first lefty is the second or third person.
d. There are exactly 3 lefties in the group.
e. There is at least 1 lefty in the group.
f. There are no more than 3 lefties in the group.
II. If we select 5 people at random,
a. How many lefties do we expect?
b. With what standard deviation?
c. If we keep picking people until we find a lefty, how long do you expect it will
take?
2.
3.
General Addition Rule: P(A  B) = P(A) + P(B) – P(A  B).
We add the probabilities of two events and then subtract out the probability of their
intersection.
Multiplication Rule For two independent events A and B, the probability that both A and
B occur is the product of the product of the probabilities of the two events.
P(A ∩ B) = P(A) x P(B), provided that A and B are independent.
If P(A) = 0.4 and P(B) = 0.2, P(A  B) =
4. Insurance company records indicate that 12% of all teenage drivers have been
ticketed for speeding and 9% for going through a red light. If 4% have been ticketed
for both, what is the probability that a teenage driver has been issued a ticket for
speeding but not for running a red light?
5. A survey of an introductory statistics class in Autumn 2003 asked students
whether or not they ate breakfast the morning of the survey. Results are as
follows:
Sex/Breakfast Yes
No
Total
Male
66
66
132
Female
125
74
199
Total
191 140
331
a. What is the probability that a randomly selected student is female?
b. What is the probability that a randomly selected student ate breakfast?
c. What is the probability that a randomly selected student is a female who ate
breakfast?
d. What is the probability that a randomly selected student is female, given that
the student ate breakfast?
e. What is the probability that a randomly selected student ate breakfast, given
that the student is female?
f. Does it appear that whether or not a student ate breakfast is independent of
the student’s sex? Explain.
6. Expected Value:
Variation:
σx =SD(X) = Var(X)
Adding & Subtracting Expected Values and Standard Deviations
E(X + Y) = E(X) + E(Y)
Var(X + Y) = Var(X) + Var(Y)
7. Some marathons allow two runners to “split” the marathon by each running a half marathon.
Alice and Sharon plan to split a marathon. Alice’s half-marathon times average 92 minutes with
a standard deviation of 4 minutes, and Sharon’s half-marathon times average 96 minutes with a
standard deviation of 2 minutes. Assume that the women’s half-marathon times are
independent. The expected time for Alice and Sharon to complete a full marathon is 92 + 96 =
188 minutes. What is the standard deviation of their total time?