50:50
Welcome to
Who Wants to
be a Millionaire
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
Another
Presentation
© 2000 - All rights Reserved
[email protected]
© Mark E. Damon - All Rights Reserved
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
A ____ of a real situation is an
experimental model of the
situation that attempts to capture
all aspects of the situation that
affect all outcomes.
50:50
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
A: simulation
B: probability distribution
C: trial
D: expected value
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
Consider rolling a single fair
die. Let A be the event {1, 2, 3}
and B be the event {2, 4, 5, 6}.
Find P(A∩B).
50:50
A: 1
B: 1/6
1/6
B:
C: 6
D: 5/6
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
How many five letter words
can be formed from the
letters of the word
CENTRAL?
50:50
A: 42
B: 120
C: 2520
D: 5040
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
Suppose a bag contains 5 balls
number 1 through 5. In how
many ways can you select 5
balls from the bag if there is no
replacement after selection?
50:50
A: 15
B: 120
C: 2520
D: 3125
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
The Kansas schools are competing to be
state basketball champions. Indicate
which is true of the following events:
Event 1: Central girls win 4A state title.
Event 2: Circle girls win 4A state title.
50:50
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
A:
Events are complementary
B: Events are mutually exclusive,
C:
Events are independent
D:
but not complementary
Events are independent &
mutually exclusive
© Mark E. Damon - All Rights Reserved
the $1,000
Milestone!
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Solve: nP7 = 6nP5
50:50
A: 3
B: 8
C: 9
D: 10
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
A test has 10 true-false questions. If
you know three answer and guess
on seven, what is the probability
that you will get them all correct?
50:50
A: 1/49
B: 1/100
C: 1/128
D: 1/1024
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
During the 1996-1997 season, Michael
Jordan made 83.3% of the free throws
he attempted. Assume independence of
free-throw attempts and find the
probability that MJ would make two of
two free throws.
50:50
A: ≈ 0.028
B: ≈ 0.25
C: ≈ 0.694
D: ≈ 0.833
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
A researcher collects the following data about
the incubation time of a certain disease.
Find the mean incubation time.
50:50
A: 3.5 days
B: 4.5 days
C: 4 days
D: 5 days
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
Let
P(A) = .5, P(B) = .2, and
P(AUB) = .6
Which of the following
applies to the events?
50:50
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
A: independent
B: mutually exclusive
C: complementary
D: A and C
© Mark E. Damon - All Rights Reserved
the $32,000
Milestone!
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Evaluate
76!
72!
50:50
A: 2,216,980,800
B: 24
C: 30,791,400
D: 1.056
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
Susan has a choice of n math
classes, five science classes
and two history classes. In how
many ways can she select one
of each of the three kinds of
classes?
50:50
A: 10n
B: 10n
C: 240n!
D: 5040n!
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
P(E) = 1 means that event E ….
50:50
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
A: Must Always Occur
B: Is Impossible
C: Has Occurred
D: Has
77.54Not Occurred
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
In a lottery, 120 tickets are sold at
$1 each. First prize is $50 and
second prize is $20. Find the
expected value of a ticket.
50:50
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
A: ≈ - 41.7¢
B: ≈ - $1
C: ≈ $22.33
D: not enough information
© Mark E. Damon - All Rights Reserved
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
Fifteen percent of the students at a
military academy are female. If
three students at this academy are
selected at random, what is the
probability that they are of the
same gender?
50:50
A: 0.0021
B: 0.6141
C: 0.45
D: 0.6175
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
$1 Million
$500,000
$250,000
$125,000
$64,000
$32,000
$16,000
$8,000
$4,000
$2,000
$1,000
$500
$300
$200
$100
© Mark E. Damon - All Rights Reserved
YOU WIN $1
MILLION DOLLARS!