Probability
•
Probability is the likelihood of a particular outcome occurring.
•
Example: probability of drawing a club from a deck of cards
•
Example: in an urn full of 10 red marbles and 12 black
marbles, the probability of drawing a black marble is
p
=
12
10
+
12
=
12
22
Law of Large Numbers
• As we repeat an experiment a large number of
times, the ratio of the number of successes in
the sample to the total number of trials will
approach the probability of the event.
• Example: proportion of heads should go to .5
10 coins:
7 H
3 T
p = .7
100 coins:
53 H
47 T
p = .53
1000 coins:
498 H
502 T
p = .498
10000 coins:
5002 H
4998 T
p = .5002
Types of Probabilities
• Classical/Relative Frequency
• Subjective
– Likelihood of an event is based on your own
personal judgment
Probability Definitions
• A complement
– All possible events
that are
not
in A
• Example:
– A = it’s snowing
– A
c
= it’s not snowing
Example of a Complement
•
We have a total of 50 seats in a room, and a shaded square above
represents a taken seat.
•
How many people are in this room?
•
It’s easier to instead count the number of empty seats, of which there
are 4. Therefore the number of people is 50 - 4 = 46
•
So the complement here is “all empty seats” which gives us the needed
answer more easily.
Probability (HW 5.1-5.3)
•
The game Scrabble contains 100 lettered tiles: 56 consonants,
42 vowels, and 2 blanks. The 42 vowels can be further classified
as follows: 9 A’s, 12 E’s, 9 I’s, 8 O’s, and 4 U’s. Suppose we
reach into a bag containing all the tiles and select one letter.
•
What’s the probability of drawing a tile with a letter on it?
–
98 such tiles, so 98/100 = .98
•
If we draw a vowel, what’s the probability it’s in the upper half of
the alphabet? (Meaning A - M)
–
Out of 42 vowels, the A’s, E’s, and I’s count, so
•
If the tile drawn contains a letter on it, what’s the probability that
letter is not a vowel?
Out of 98 letters, 56 of them are not vowels.
9
+
12
+
9
42
=
30
42
=
.714285
56
98
=
.57143

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*Sign up*Probability (HW 5.1-5.3)
We have an urn full of marbles of the following colors: 5 green,
4 blue, 3 yellow, 2 red, 1 white (15 total).
What’s the probability of drawing a primary color? (Red, yellow, or
blue)
If the marble drawn was a primary color, what’s the probability it was
either red or yellow?
Out of 9 primary color marbles, we have 2 red
and 3 yellow, so
If the marble drawn was not a primary color, what’s the probability it
was not green?
2
+
3
+
4
15
=
9
15
=
.6
2
+
3
9
=
5
9
=
.55556
There are 6 non-primary color marbles: 5 green, 1 white.
So, out of 6 marbles, 1 is not green (the white).
1
6
=
.16667
Probability (HW 5.1-5.3)
•
The ice cream HW question again!
•
Find the probability that an individual selected is female and prefers
strawberry ice cream.
Out of all 2176, we have 302 that are both female
and like strawberry, so 302 / 2176 = .13879
•
Find the probability that an individual selected is female or prefers
strawberry ice cream.
Out of 2176 again. We count the number who are
either female or like strawberry, or both. (As long as they have at least
one of the two characteristics, we count them.) As indicated above, this

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