Flipping a coin 10,000 times
When there have been few flips, Pe (H) can vary wildly.
As the number of flips increases, Pe (H) settles around a number.
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Example 10.1
Open your book to a random page and recording the right-hand
page number twenty times:
Calculate Pe (a right-hand page number is divisible by 3).
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Example 10.2
Calculate Pe (a HS boy’s height is between 68 and 70).
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Example 10.3
Given 28 grades from the final in a calculus course:
Calculate Pe (a student got a C).
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Example 10.4
Flipping 5 coins at once, fifty times:
Number of heads
Frequency
0
1
1
7
2
13
3
16
4
11
5
2
Calculate Pe (at most 1 head).
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Sample Space and Events
Our experiment is adding the sum of
two rolled dice.
Sample space:
S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
Event A - rolling a 7
Event B - rolling an 11
Event E = A∪B - rolling a 7 or an 11
Note:
A ∪ B is the same as ‘A or B’. A ∩ B
is the same as ‘A and B’.
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Example 10.5
Roll a pair of dice 50 times:
Roll
Count
2
1
3
0
4
3
5
4
6
10
7
12
8
8
9
4
10
4
Compute Pe (7), Pe (11), Pe (7 or 11).
Show that: Pe (7 or 11) = Pe (7) + Pe (11).
MA202 Sections 5 & 401
Chapter 10-1 Graphs
11
2
12
2
Example 10.6
Flipping a penny and a dime together 50 times:
Let A be the event of the dime landing heads up.
Let B be the event of both coins landing with the same side up.
Calculate Pe (A), Pe (B), Pe (A ∪ B).
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Example 10.7
Flipping a penny and a dime together 50 times:
Let A be the event of the dime landing heads up.
Let B be the event of the penny landing heads up.
Calculate Pe (A), Pe (B), Pe (A and B).
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Example 10.8
Estimate Pe (A), Pe (B), Pe (C ).
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Class Discussion
Does a 30% chance of rain mean that it will rain for 30% of
the day? If not, what does it mean?
Of the basic eye colors, Pe (blue) = .1, Pe (brown) = .2,
Pe (hazel) = .4, Pe (green) = .3. What is the probability that
for a married couple, both spouses have hazel eyes? The
probability one spouse has brown eyes and the second has
green?
Number 15 in the book (if we have time)
MA202 Sections 5 & 401
Chapter 10-1 Graphs
Homework
Homework 3 (due 2/23/09):
Section 10.1 # 1, 6, 8, 19, 20, 28, 32
Section 10.2 # 3, 4, 6, 9, 15, 18, 23, 28, 37
MA202 Sections 5 & 401
Chapter 10-1 Graphs