Review
• Probability
• Random variables
• Binomial distribution
1
1. Event A occurs with probability 0.2. Event B occurs with
probability 0.8. If A and B are disjoint (mutually
exclusive) then
(i) p(A and B)=0.16 (ii) p(A or B)=1 (iii) p(A and B)=1
(iv) p(A or B)=0.16
2. Ignoring twins and other multiple births, assume babies
born at a hospital are independent events with
probability that a baby is a boy and that a baby is a girl
both equal to 0.5. The probability that the next 5 babies
are girls is:
(i) 1 (ii) 2.5 (iii) 0.25 (iv) 0.03125 (v) 0.5
2
3. In a certain town 50% of the households own a cellular
phone, 40% own a pager and 20% own both a cellular
phone and a pager. The proportion of households that
own neither a cellular phone nor a pager is
(i) 10% (ii) 30% (iii) 70% (iv) 90%
4. Event A occurs with probability 0.3 and event B occurs
with probability 0.4. If A and B are independent, we may
conclude that
(i) p(A and B)=0.12 (ii) p(A|B)=0.3 (iii) p(B|A)=0.4 (iv)
all of the above
3
5. Of all children in a juvenile court, the probability of
coming from a low income family was .60; the
probability of coming from a broken home was 0.5; the
probability of coming from a low-income broken home
was 0.40
(i) what is the probability of coming from a low-income
family or broken home (or both)?
(iii) find the probability of coming from a broken home,
given that it was a low income family. Are the two
events low-income and broken home independent?
4
6. Jane and Tim prepare their wedding invitations by
themselves. Jane works faster and prepares 80% of the
invitations. However 10% of her invitations turn out with
some mistakes. Out of Tim’s invitations, only 1% have
mistakes.
(iii) What is the probability of an invitation has a mistake
in it?
(iv) Given that an invitation has a mistake, what is the
probability that it has been written by jane?
5
7. A certain university has the following probability distribution for
number of courses X taken by seniors in their final semester
courses 1 2 3 4 5 6
Probability .05 .10 .30 .40 .10 .05
(i) What is the probability that a randomly chosen senior took at least
4 courses in the final semester?
(ii) what is the probability that a randomly chosen senior took more
than 4 courses in the final semester?
(ii) The shape of the distribution of number of courses is: skewed left
/ skewed right / symmetric but not at all bell-shaped / reasonably bell
shaped
6
8. A surprise quiz contains 3 multiple choice questions. Question 1 has
three suggested answers, Question 2 has three suggested answers,
and question 3 has two. A completely unprepared student decides to
choose the answers at random. Let X be the number of questions that
the student answers correctly.
a. List the possible values of X
X=0,1,2,3
b. Find the probability distribution of X.
Q1-first is correct p(Q1)=1/3 Q2-second is correct p(Q2)=1/3
Q3-third is correct p(Q3)=1/2
7
9. In a particular game, a fair die is tossed. If the number of
spots showing is either 4 or 5 you win $1, if number of
spots showing is 6 you win $4, and if the number of
spots showing is 1,2, or 3 you win nothing. Let X be the
amount that you win. The expected value of X (mean of
X) is:
i) $0.00 (ii) $1.00 (iii) $2.50 (iv) $4.00
8
10. A small store keeps track of the number X of customers
that make a purchase during the first hour that the store is
open each day. Based on the records, X has the following
probability:
X 0 1 2 3 4
P(x) 0.1 0.1 0.1 0.1 0.6
The mean number of customers that make a purchase
during the first hour that the store is open is
i) 2 (ii) 2.5 (iii) 3 (iv) 4
9
11. 8% of males are color blind. A sample of 8 men is taken
and the number X of people that are color blind are
counted.
What is the probability to find 4 people that are color blind
in the sample?
what is the probability that at least 7 people in the sample
are color blind?
10