Review For Probability Test
1. Which of the following values
cannot be probabilities?
3 5
0, 1,  1, 2, 0.0123, , , 2
5 3
2. In the New York State Lottery, you
have to select six numbers between 1
and 54 inclusive. There are 25,827,154
different possible six number
combinations.
What are your chances of winning the
grand prize (all six correct numbers) if
you buy 100,000 tickets each with
distinct number combinations? Round
your answer to 3 decimal places.
0.004
3. Assuming that boys and girls are equally likely, a
couple had four children one at a time. The first was
a boy; the second was a boy; the third was a boy and
the forth was also a boy. Now they are expecting
their 5th baby. They still don’t know the sex of the
baby but they do know that it is not a multiple birth.
what is the probability that there fifth baby is also
a boy?
0.5
4. An American household is chosen at
random and asked how many cars and
trucks that household owns. Here are
the probabilities as of 1997:
This is a legitimate assignment of probabilities
because it satisfies these rules:
(a) all the probabilities are between 0 and 1.
(b) all the probabilities are between -1 and 1.
(c) the sum of all the probabilities is exactly 1.
(d) Both (a) and (c).
D
5. What is the probability that a
randomly chosen household owns
more than one motor vehicle?
(a) 0.96
(c) 0.26
(b) 0.71
(d) 0.25
B
6. It is common for public opinion
polls to have a confidence level of
95%, meaning that there is a 0.95
probability that the poll results are
accurate within the claimed margins
of error. If five different organizations
conduct independent polls, what is
the probability that all five of them are
accurate within the claimed margins
of error? (Round to 3 decimals)
0.774
7. For Yorktown students, there are only five different
restaurants to go for lunch: Wendy’s, Bagel Bakery,
Taco Bell, Harris Teeter and Subway. Each restaurant
is independent of each other and students can only go
one place for lunch. The probability of a student
going to Wendy’s is 0.27, Bagel Bakery is 0.32, Taco
Bell is 0.12, and Harris Teeter is 0.08.
a.What is the probability of a student going to
Subway for lunch?
.21
b.What is the probability of a student going to a
“fast food” restaurant for lunch? (Wendy’s or
Taco Bell)
.39
NO
8. Decide whether events A and
B are mutually exclusive.
NO
A- Being left handed
B - Being female
A- Rolling a dice and getting a 6
B – Rolling a dice and getting an odd
number
A – Being born in July
B - Being born in 1990
Yes
P(A) = 4/15 and P(B) = 6/15
P (A or B) = 10/15
Yes
9) A bag contains 15 marbles; four are red, five are
green, six are yellow. (Answer in decimal form)
– a.If one marble is randomly selected what is the
probability that it is not red?
11/15=.73
– b.
If one is randomly selected, what is the
probability that it is red or green?
9/15=.6
– c.If one is randomly selected, what is the
probability that it is not blue?
15/15=1
10. A single playing card is randomly drawn
from a standard deck of 52 cards.
(Decimal Answers)
a.
What is the probability that it
is an Ace? 4/52=.08
b.
What is the probability that it
is a red card?
26/52=.5
c.
What is the probability that it
is a jack or a spade?
16/52=.31
d.
What is the probability that it
is not a 6 or a diamond?
36/52=.69
Review Game Rules:
• One chance per question!
• In order to get credit for the
question, you need to show both the
set up and the final answer in
percent or decimal form!
• First correct Answer gets 2
• Second correct Answer gets 1
• Answers need to be presented on
the white boards!
11.
I What is the probability of rolling two dice and
getting a total of six?
C
II. What is the probability of getting a total of
seven?
D
III. What is the probability of getting a total of 2
or three?
A
12.
Six cards are randomly drawn from a
standard deck without replacement. What is the
probability that at least one of them is a club?
Decimal Answer
1-(39/52)(38/51)(37/50)(36/49)(35/48)(34/47)=.84
13. Four firms using the same
auditor independently and randomly
select a month in which to conduct
their annual audits. What is the
probability that the months are the
same for all four auditors?
Decimal Answer
(12/12)(1/12)(1/12)(1/12)=.00058
14. Ten percent of us are left
handed. What is the probability
that 8 randomly selected people
will all be right handed?
Decimal Answer
(.9)^8=.43
15. True or False? If you were to roll a
fair dice 1,000 times, the
proportion of six’s rolled will be a
lot closer to 0.17 than if you were
to do it only 5 times.
TRUE!!!!
16. A classic excuse for a missed test is
offered by four students who claim that
their car had a flat tire. On the makeup
test, the instructor asks the students to
identify the particular tire that went flat. If
they really didn’t have a flat tire and
randomly select one that supposedly went
flat, what is the probability that they will all
select the same tire? Decimal Answer
(4/4)(1/4)(1/4)(1/4)=.016
17. If a couple plans to have eight
children, find the probability that
they have at least one boy.
Decimal Answer
1-(1/2)^8=.996
18. What is the probability that no
two people have the same birthday
when the number of randomly
selected people is 4????
Decimal Answer
(365/365)(364/365)(363/365)(362/365)=.984
19. An employee needs to call any one
of five colleagues. Assume that the
five colleagues are random selections
from a population in which 28% have
unlisted numbers. Find the
probability that at least one of the
five fellow workers will have a listed
number.
Decimal Answer
1-(.28)^5=.998
20. There is a 0.63 probability
that Mobil stock will rise, a 0.75
probability that Gulf stock will
rise, and a 0.47 chance that both
stocks will rise. Find the
probability that neither stock will
rise.
.2775
21. A typing pool is made up of
five men and five women. If
three different typists are
randomly selected from the pool,
find the probability that at least
one of the three is a man.
Decimal Answer
1-(5/10)(4/9)(3/8)=.92