Name______________
Date____________
IB Math Studies
Probability Review
1.
2.)
3.) A survey was given to people shopping at Sears in December and January. It asked what type of item
they were shopping for? The table below represents the results.
Type of Item
Tool
Clothing
Appliance
Jewelry
Total
December
578
315
151
176
1220
January
312
198
142
86
738
A. What is the experimental probability that a person visiting Sears is shopping for a
tool?
B. What is the experimental probability that a person visiting Sears in December is not
shopping for an appliance?
4.) During the snow season there is a 3/7 probability of snow falling on any particular day. If Udo skis for
6 weeks, on how many days could he expect to see snow falling?
5.) A person plays a game with a pair of coins. If two heads appear then $20 is won. If a head and a tail
appear in any order then $4 dollars is won. If two tails appear then $1 is won. What is the expected
value of each coin flip?
6) If P(D) = .6 , P(E) = .4 and P(D U E) = .8, find P( D ∩ E).
7.) The average height of 17 year old boys is normally distributed with mean 179 cm and
standard deviation 8 cm. Sketch the normal distribution curve for this situation.
Calculate the percentage of 17 year old boys whose heights are(without a calculator):
A. More than 195 cm.
B.) between 163cm and 187cm
C. Between 171 cm and 187cm.
Calculate the percentage of 17 year old boys whose heights are(with a calculator):
D, Less then 168cm.
E. Between 160cm and 180cm.
8.) Suppose 𝑋~𝑁(150, 122 ) Find:
A. P(138 < X < 162)
B. P(X < 147)
9.) In a competition to see who could hold their breath underwater the longest, the times were
normally distributed with a mean of 150 seconds and standard deviation 12 seconds. The top
15% of contestants go through to the finals. What time is required to advance to the finals?
Final Exam Review
1.) Students at Palmer High School were surveyed about the length of their bus ride to school. The
information from this survey is presented on the histogram below.
Number of Students
40
Number of Students
35
30
25
20
15
10
5
0
0 < x ≤ 10
10 < x ≤ 20
20 < x ≤ 30
30 < x ≤ 40
40 < x ≤ 50
50 < x ≤ 60
Length of Bus Ride
(minutes)
A. About how many students were surveyed?
B. Write down the modal class.
C. What is the mid interval value of the
20 < x < 30 class.
D. What is the probability that a student chosen
at random will have a bus ride that is
between 20 and 40 minutes inclusive.
E. Complete the frequency table for this distripution.
Lenge of Bus
Ride (In
Number of
Minutes)
Students
0 < x ≤ 10
10 < x ≤ 20
20 < x ≤ 30
30 < x ≤ 40
40 < x ≤ 50
50 < x ≤ 60
2.) The data below represent a survey where couples without kids were asked how
many children they planned to have.
0, 0, 4, 2, 3, 3, 2, 3, 2, 1, 5, 3, 1, 2, 0, 3, 4, 0
A.) What type of data is this?
A. Categorical
B. Quantitative Discrete
C. Quantitative Continuous
D. False data
B.) Represent the data with a Box and Whisker Plot
D.) Calculate the Mode=______, the Mean = ______ and the Median = _______
E.) Calculate the standard deviation.
F.) Calculate the interquartile range.
G.) Mr. Kroon Estimated the average number of children couples planned to have was
2. Calculate the percentage error on Mr. Kroon estimate.
2. Given the sequence 5, 16, 27, 38…
A. What type of sequence is this?
C. Give a formula for the general term.
E. Give the sum of the first 15 terms
B. Give the next term in the sequence.
D. Find the 10th term. (do not round the
answer)
3. Determine the number of terms in the sequence then find the sum of the sequence.
6, 11, 16, 21… 116
4. Given the formula for the general term of U n  3n  4
A. What type of sequence is this?
B. List the first 4 terms.
15
13. Evaluate
 6n  11
n 1
5. If you invested this years PFD of $891.23 in an account paying 6% p.a. compounded
quarterly, how much interest will you make in 15 years?
6. A. In 2012, 4120 students graduated from high school. This number increases by
1.5% each year. How many students will graduate in 2020?
B. How many total students graduated in the years from 2012 to 2018?
7. Use set builder notation to describe the set of all integers between -15 and 10
8. There were originally 4501 Kangaroo’s on Australia. Since then, the population of koalas on
the island has increased by 2% each year.
A. Write an equation represent the koala population.
B. What is the koala population after 5 years?
C. How long does it take the koala population to reach 5000?
9. Label and shade the region described on a venn diagram.
A. A’ U B
B. 𝐴 ∩ 𝐵′
C. (A U B)’
.
10. Given n(U) = 15, n(G)= 6, n(H) = 8 and n(𝐺 ∩ 𝐻) = 2 .Find:
A. n(in H, but not in G)
B. n( (G U H)’)=
C. n( G U H)
11. Convert 35 km/h to m/s.
12. Consider the propositions:
p: I love swimming
Write the statements below in words.
A. ¬ p => q
q: I have a pool
B. q Ʌ ¬ p
13.) Complete the truth table below
p q p V ¬q ¬𝑞 𝑞 =>¬q ¬p Ʌ q
T T
T F
F T
F F
(¬p Ʌ q) Ʌ 𝑞
14. Write the argument below in symbolic language
All dogs have eyes
Rover has eyes
Hence, Rover is a dog
15. Complete the truth table below to determine if the argument in number 9 is a valid
argument.
p
T
T
F
F
q
T
F
T
F
*16.) Fred is going home to Vietnam after Working in Singapore. he has 4000 Singapore dollars (SGD)
and changes these into American dollars (USD) to take home. The exchange rate between Singapore
dollars (SGD) and American Dollars (USD) is
1 USD = 1.2831 SGD
There is also a 3.1% commission on the exchange.
A. Calculate the amount of commission on the exchange in SGD
B. Calculate the number of American Dollars (USD) Fred takes home.
Give your answer correct to 2 decimal Places.
At the airport in Vietnam, Fred changes 150 USD into Vietnamese dong (VND) to pay for his transport
home. The exchange rate between American dollars (USD) and Vietnamese dong (VND) is
1 USD = 18945 VND
There is no commission.
C. Calculate the number of Vietnamese dong that Fred receives. Giver your answer correct to
the nearest thousand dong.