What you should learn
To find the probability of a simple event To find the odds of a simple event NCTM Curriculm Standards 2, 5 - 10
To find the probability of a simple event
To find the odds of a simple event
NCTM Curriculm Standards 2, 5 - 10
In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:
Probability Probability of an Event Random
Probability
Probability of an Event
Random
Introduction: Have you ever heard anyone say that one man's trash is another man's treasure? For garbage truck driver Craig Randall of East Bridgewater, Massachusetts, the treasure was a hamburger chain's soft-drink cup. By peeling off a contest sicker on the discarded cup, Randall won the grand prize of $200,000 toward the purchase of a home! Since there was only one grand price available and 24,059,900 cups were distributed, the probability of winning the grand prize was 1/24,059,900.
You can calculate the chance, or probability, that a certain event, such as a winning a particular prize, will happen. The probability of an event is a ratio of the nubmer of ways a certain event can occur to the number of possible outcomes. The numerator is the number of favorable outcomes, and the denominator is the total number of possible outcomes.
For example, suppose you want to know the probability of getting a 2 on one roll of a die. When you roll a die, there are six possible outcomes. Of these outcomes, only one is favorable, a 2. Therefore, the probability is 1/6. We write P(2) to represent the probability of getting a 2 on one roll of a die.
Definition of Probability: P(event) = number of favorable outcomes/total number of possible
Exercise 1: Lauren is representing her sophomore class in a word board game tournament. She is the first player to select her seven tiles out of the 100 available tiles. The distribution of tiles is shown at the right. Find the probability of each selection.
J, K, Q, X, Z
B, C, F, H, M, P, V, W, Y, blank
G
D, L, S, U
N, R, T
O
A, I
E
1
2
3
4
6
8
9
12
a. An O on the very first selection. There are eight O tiles and 100 tiles in all. P(selecting an O) = 8/100 or 2/25 The probability that Lauren selects an O is 2/25 or 8%. b. An E if 5 tiles have been selected and 2 of them were Es. There are 12 E tiles. If 2 have been chosen, 10 remain. There are 100 - 5 or 95 tiles from which to select. P(choosing an E) = 10/95 or 2/19 The probability of selecting an E is 2/19 or about 10%.
a. An O on the very first selection.
There are eight O tiles and 100 tiles in all. P(selecting an O) = 8/100 or 2/25 The probability that Lauren selects an O is 2/25 or 8%.
There are eight O tiles and 100 tiles in all. P(selecting an O) = 8/100 or 2/25
The probability that Lauren selects an O is 2/25 or 8%.
b. An E if 5 tiles have been selected and 2 of them were Es.
There are 12 E tiles. If 2 have been chosen, 10 remain. There are 100 - 5 or 95 tiles from which to select. P(choosing an E) = 10/95 or 2/19 The probability of selecting an E is 2/19 or about 10%.
There are 12 E tiles. If 2 have been chosen, 10 remain. There are 100 - 5 or 95 tiles from which to select.
P(choosing an E) = 10/95 or 2/19
The probability of selecting an E is 2/19 or about 10%.
The probability that an event will occur is somewhere between 0 and 1.
A probability of 0 means that it is impossible for an event to occur A probability of 1 means that an event is certain to occur. A probability between 0 and 1 means that an event is neither impossible nor certain.
A probability of 0 means that it is impossible for an event to occur
A probability of 1 means that an event is certain to occur.
A probability between 0 and 1 means that an event is neither impossible nor certain.
Based on the situations above, the probability of any event can be expressed as 0P(event)1.
Some outcomes have an equal chance of occurring. We say that such outcomes are equally likely. When an outcome is chosen without any preference, we say that the outcome occurs at random.
Another way to express the chance of an event's occuring is with odds. The odds of an event is the ratio that compares the number of ways an event can occur to the number of ways it cannot occur.
Definition of Odds: The odds of an event occurring is the ratio of the number of ways the event can occur (successes) to the number of ways the event cannot occur (failures).
Exercise 2: Mike's Submarine Shop has a business card drawing for a free lunch every Tuesday. Four coworkers from Invo Accounting put their business cards in the bowl for the drawing. If 80 cards were in the bowl, what are the odds that one of the coworkers will win a free lunch?
The coworkers have 4 of the 80 business cards. Thus, there are 80 - 4 or 76 business cards that will not be winning cards for the coworkers. Odds of winning = number of chances of drawing winning card: number of chances of drawing other cards = 4:76 or 1:19
The coworkers have 4 of the 80 business cards. Thus, there are 80 - 4 or 76 business cards that will not be winning cards for the coworkers.
Odds of winning = number of chances of drawing winning card: number of chances of drawing other cards
= 4:76 or 1:19
Exercise 3: Refer to the application at the beginning of the lesson. The probability of winning any prize or food discount in the peel-off sticker contest was 20% or 1/5. Find the odds of winning a prize or discount.
Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.
Homework: The homework to be assigned for tonight would be: 13 - 41 odd, 42 - 49
Alternative Homework: Enriched: 14 - 36 even, 37 - 49
Extra Practice: Students book page 766 Lesson 4-6
Extra Practice Worksheet: Click Here.
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