Probability Lesson and Activities
NJ CCCS 4.1.12, 4.1.13, 4.2.10, 4.3.12
OBJECTIVE:
Students will be able to identify the number of favorable outcomes and possible
outcomes in an event. Students will be able to calculate the probability that an
outcome will occur.
WARM-UP ACTIVITY: Draw a large circle wheel on oak tag. Divide it into as
many equal wedges as you can. (Hopefully each student will do a different number
of wedges.) When the students divide their circles, they will name each wedge.
Give examples: favorite names, colors, numbers, etc. Students create an arrow
made from oak tag to put in the circle's cente r. This becomes the spinner.
Student's answer, "When I spin the arrow, how likely is it that the arrow will
land on a given wedge?" What is the probability? Students describe the number of
possible results in each spin. They also write in their journals what happens.
TEACHING STRATEGIES: Students need to understand the essentials about the
concept of probability (P): P expresses the likelihood that the desired outcome
will occur. Each possible outcome is equally likely to occur in any given trial.
P is a ratio of the desire d outcome to the number of possible outcomes.
Students explain why the probability of an event cannot be greater than 1. (You
cannot have more successes than tries.)
Materials Needed: Oak tag,
scissors, paper clips, crayons, markers, rulers, pencils, etc.
The students have explored the mean, median, and mode of a set of data. These
are examples of statistics. Statistics also include probability-the chance or
likelihood that an outcome will occur. Probability experiments always include an
event and one or more outcomes. To find the probability (P) that an outcome will
occur, use the fraction:
P = number of favorable outcomes /number of possible outcomes.
Probability Using a Coin: Suppose a coin is tossed once. What is the probability
(P) that the coin will land heads up? Students chart their answers and write
about the outcomes. Use the probability fraction. Find the denominator. Since
there are two possible outcomes when the coin is tosses-the coin will land
either heads up or tails up-the denominator is two. Find the numerator. Since
one outcome is favorable-the coin landing heads up-the numerator is one. P = ½
The probability of tossing a coin and having it land heads up is ½. Since they
will discover how to change a fraction to a percent, they can also say that the
probability of flipping a coin and having it land heads up is 50%. This is
because ½ = 50%. Students will do this many times and chart their results. They
will write about their discoveries. They can also do this with dice.
USING MANIPULATIVES: Probability Experiment
Materials: 1-6 Number Cubes
Group Practice: Students
use a number cube to conduct a probability experiment. They roll the number cube
10 to 20 times, having other students record the number that comes up with each
roll. Show the students how to use this data to describe the actual outcome of
the event as a fraction in simplest form. Students use the cubes in the same way
to conduct their own probability experiments with their circle wheels.
TECHNOLOGY CONNECTION: Cell Phones + Pagers = More Phone Numbers The
number of ways we can "reach out and touch" one another continues to multiply.
Less than a decade ago, there was usually one telephone number per household.
Now a household may have a phone line for the computer, two or three cell phones
cell phones, and a pager. All of these lines need a number different from the
regular phone line. Phone companies began running out of numbers. The solution
was to add more area codes. Adding just three digits has increased the
combinations of phone numbers by the millions.
CONTINUED OBJECTIVE: Students will be able to classify outcomes as
certain, impossible, very likely, not likely, more likely, or less likely.
Students will be able to calculate probability of events and their complements.
WARM-UP ACTIVITY: Students conduct a poll to find out which radio
stations classmates listen to. Students design a form listing radio stations on
the left and a range of responses on the right. List the choices participants
should be able to circle (e.g., always, never, almost always, almost never,
sometimes). Students will order the responses. They place the responses on a
line and ask students which end correlates to a probability of 0 and which to a
probability of 1.
TEACHING STRATEGIES: Explain that complement is the amount or number
needed to fill or complete. Students will create an equation that expresses the
relationship between a probability and its complement. P1 (desired outcome) + P2
(all other outcomes) = 1 (total possibilities), where P1 and P2 are
probabilities.
PROJECTS: Let the students complete these and discover the conclusion
that is listed. Have them write their results and explanation in their journals.
EXAMPLE 1: Suppose the student rolls a 1-6 number cube once and looks for an
outcome of 1, 2, 3, 4, or 5. They are very likely to be successful because there
are five favorable outcomes ( 1, 2, 3, 4, 5) in the event and only one
unfavorable outcome (6). EXAMPLE 2: Suppose the student rolls a 1-6 number cube
once and looks for an outcome of 6. They are not likely to be successful because
there is only one favorable outcome (6) in the event and five unfavorable
outcomes (1, 2, 3, 4, 5). EXAMPLE 3: Suppose each letter of the alphabet is
written on a slip of paper. All the slips of paper are the same size and are
folded in the same way. Have a student choose one slip without looking. That
student is more likely to choose a consonant than a vowel because there are 21
consonants and only 5 vowels in the alphabet. Also, they are less likely to
choose a vowel than a consonant for the same reason.
COMBINING BOTH OBJECTIVES: What is the probability of tossing a coin and
not getting an outcome that is heads? Use the probability fraction
P = number of favorable outcomes/number of possible outcomes
Students find the denominator. Since there are two possible outcomes when the
coin is tossed-the coin will land either heads up or tails up-the denominator is
two.
P = number of favorable outcomes/2
Students find the numerator. Since they are looking for an outcome that is not
heads, the outcome that is favorable is tails. There is one favorable outcome.
P = ½
The probability of tossing a coin and not getting an outcome that is heads is ½.
It is also an example of the complement of the probability event. The complement
of a probability event is the set of outcomes that are not in the event.
HOMEWORK OR EXTRA PRACTICE:
EXAMPLE 1 Use one of these words or phrases to complete each sentence:
certain, impossible, very likely, not likely, more likely, less likely.
1. The probability of tossing a coin and getting an outcome of heads or tails is
______________. (answer-certain)
2. It is ___________________that a person was born during t he month of
February. (answer-not likely)
3. An outcome of 2 or 4 on a 1-6 number cube is ______________than an outcome of
any odd number. (answer-less likely)
EXAMPLE 2 Given a spinner, which is divided into 8 colored wedges,
students express the probability of each event as a fraction in simplest form.
1. P (blue) Answers: 1. (1/2); 2. ((1/4); 3. (3/4);
2. P (orange) 4. (5/8); 5. (1/2); 6. (1/4); 7. 3/8);
3. P ( not green and not white) 8. (3/4); 9. (7/8)
4. P (blue or white)
5. P (green or not blue)
6. P (white or green)
7. P (not white and not blue)
8. P (not orange)
9. P (not white)
EXAMPLE 3 Students answer the following questions using all that they
learned. The Football Team is having a raffle to raise money for uniforms. Two
hundred tickets have been sold at $10 a ticket. The holder of the winning ticket
will receive a free seasons pass for all games-worth $100.
1. Find the probability that the stud ent will not win if you buy one ticket.
2. Decide what chance of winning (certain, very likely, more likely, less
likely, not likely, or impossible) if the student: a. will buy 10 tickets
(answer-not likely); b. will buy2 tickets (answer-not likely); c. will buy no
tickets (answer-impossible); d. will buy 180 tickets (answer-very likely)
3. Students write a paragraph explaining why it is foolish to buy 10 tickets.
EXAMPLE 4 Determine the probability in each of the following problems.
a. Suppose your teacher randomly selects a student from your class. What is the
probability that the student selected is you? (answer- __________1____________
(number of students in the class)
b. Suppose your teacher randomly selects a student from your class. What is the
probability that the student selected is not male?
(Answer- (number of females)
(total number of students)
EXAMPLE 5 How many different outcomes are possible if two 1-6 number
cubes are rolled? What is the probability of rolling 6 with each cube?
(answer-36 different outcomes; 1/36)
WRITING ABOUT MATHEMATICS: Students will predict their results of tossing
a coin 20 times. They might expect to get 10 heads and 10 tails in 20 coin
tosses. They toss a coin 20 times. They tally their results. They compare their
results to their prediction. Write their findings in their journal.
More probability
activities:
http://www.lhs.logan.k12.ut.us/~jsmart/prob1.htm
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