MDM4U: Unit 1 Probability and Counting Test
Knowledge and
Application /24
Communication /6
Thinking Inquiry /
8
Total out of 38
Knowledge / Application
1. Determine the number of ways from point A to point B.[2 marks]
2. There are 52 cards in a standard d
The CENTRE for EDUCATION
in MATHEMATICS and COMPUTING
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2012 Euclid Contest
Wednesday, April 11, 2012
(in North America and South America)
Thursday, April 12, 2012
(outside of North America and South America)
Solutions
2012 University
\ _
Unit
:./
MDM4U / Review Package Probability
Remember: This review package is only an overview of the main topics covered this semester. For the final exam, you are
responsible for ALL topics covered throughout the course.
Key Ideas: |
The Birthday Problem
Find the probability that in a group of n ( n 365) people, at least two people share the same birthday.
Here n = 23 (and n = 106), but lets solve this rst for general n. We assume that all 365 days of the
year (for simplicity, we igno
More MDM 4U Probability Review
1. Microchips being manufactured have a 28% chance of not working when they come off the
production line. Of the not working microchips, 79% can be repaired and the rest are considered
defective.
a) What is the theoretically
Birthday Paradox
Yue Kwok Choy
(1) Introduction
Please make a guess:
In a class of 23 students, what is the
probability that at least two students sharing a birthday, assuming that there
are 365 days in a year (forget about the leap year) ?
This is the cl
r=
r=
n (Xi Yi) XiYi
(n Xi ( Xi) ) (nYi (Yi) )
2
2
2
2
38(296198) (2611.5)(4317)
(38(180044.15) (2611.5)2 ) (38(510789) (4317)2 )
r 0.1413
n (Xi Yi) XiYi
a=
n Xi 2 ( Xi)2
38(296198) (2611.5)(4317)
38(180044.15) (2611.5)2
a 0.8425
b = y a
The CENTRE for EDUCATION
in MATHEMATICS and COMPUTING
www.cemc.uwaterloo.ca
Euclid Contest
Tuesday, April 12, 2011
c 2011 Centre for Education in Mathematics and Computing
Time: 2 1 hours
2
Calculators are permitted, provided they are non-programmable and
MDM4U REVIEW QUESTIONS #1: EXAM PREPARATION
WARNING: The following questions are meant to supplement your own review of the course for
the exam. Some of the concepts that we covered in the course may not come up in the following
review; however, you are s