Topic: PROBABILITY

Materials: Teaching aids, (Dice, Spinners, coins)

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LO: Students will be able to compute the probability of an event & to use concepts of probability to solve real life problems.

Do Now:

Simplify the following products so that they are more easily computed with mental math.

  1. 39 x 40 = (40 - 1) x 40 = 40 x 40 - (1) x 40 = 1600 - 40 = 1560.
  2. 101 x 99 = (100 + 1) ( 100 - 1) = 100 2- 12 = 10000 - 1 = 9999
  3. 337 / 17 = 340 / 17 - 3/17 = 20 - 3 / 17 = 19 + 17 / 17 - 3 / 17 = 19 14 / 17.
  4. If you toss a fair coin ten times , 100 times or 1000 times , in each case , how many tails would you expect ? ( 5, 50, 500) Explain? Probability of tails in each toss is ½.

Motivation:

Discussion as to why they should learn about probability.

Many events in real life are not certain. Probability can help one determine the likelihood that such events will actually occur.

Presentation of the content:

  1. Find the probability of an event.

Probability of an event is a measure of the likelihood that the event will occur. The Probability is measured on a scale from 0 to 1.

P=0

P=0.25

P=0.5

P=0.75

P=1.0

IMPOSSIBLE

(Cannot Occur)

SOMEWHAT LIKELY TO OCCUR

EQUALLY LIKELY TO OCCUR OR NOT OCCUR

QUITE LIKELY TO OCCUR

CERTAIN TO OCCUR

VOCABULARY:

TERMS AND DEFINITIONS.

AN OUTCOME:

Result of some activity or experiment. Ex: In rolling a die , 1 is an outcome, 2 is an outcome is an outcome, 3 is an outcome, and so on. There are six outcomes here.

A sample space: All possible outcomes for the activity. In rolling a die , there are six possible outcomes in the sample space.1,2,3,4,5,6.

Set notation Outcome set: {1,2,3,4,5,6}

An event is a subset of the sample space.

Ordinary Conversation - a situation or happening.

Technical Language - the subset of the sample space that lists all of the outcomes for a given situation.

Ex: an event of rolling a number greater than 4 contains only two outcomes: 5 and 6.

Another event: Rolling a number less than 5.

Outcomes: 1,2,3,4

Another event of rolling a 2 which contains only one outcome: 2 [ Whenever there is only one outcome the event is called a Singleton Event].

Theoretical probability for fair, unbiased objects.

The theoretical probability on an event is the number of ways that the event can occur divided by the total number of possibilities in the sample space.

In symbolic form, we write:

P(E) = n(E)/n(S) where

P(E) - represents the probability of an event E.

n(E) - represents the number of ways that an event may occur.

n(S) - represents the total number of outcomes in the sample space.

Find the probability of rolling a number greater than 4?

Possible outcomes: {5,6}

E= set of numbers greater than 4 = {5,6} so n(E) =2

S = the set of six possible outcomes ={1,2,3,4,5,6} so n(S)=6.

Therefore:

P(E) = n(E)/n(S)

P(E)= (number of ways to roll a number greater than 4) / (total number of outcomes for the die)

=2/6 =1/3

Uniform Probability

A sample space is said to have uniform probability, or to contain equally likely outcomes, when each of the possible outcomes has an equal chance of occurring.

So P(1) =P(2) = P(3) = P(4) = P(5) = P(6) = 1/6

Procedure for finding the simple probability of an event.

    1. Count the total number of outcomes in the sample space: n(S)
    2. Count all the possible outcomes in the event E: n(E)
    3. Substitute the values into the formulae P(E) = n(E) / n(S)

Class Work

    1. A standard deck of 52 cards is shuffled. Lilian draws a single card from the deck at random. What is the probability that the card is a Jack.

P(J) = n(J) / n(S)

    1. A Spinner contains eight regions, numbered 1 through 8. The arrow has an equally likely chance of landing on any of the eight regions. If the arrow lands on the line, it is not counted and the arrow is spun again.

n(S) =8

Coop Activity

  1. Spinning a spinner.
    1. Green 2)P® 3)Pr 4)P(b)
  1. What is the probability of choosing a letter A from the words ALABAMA. (Answer 4/7)
  2. You are taking a poll to find the blood types of 200 people. You obtain the following results:

Blood Type

Number

O+

74

A+

71

B+

17

O-

14

A-

12

AB+

6

B-

4

AB-

2

From the results of the survey, what is the probability that a randomly chosen person has the following blood type?

a)O+ b)B- c)A+ or A-

What is the probability that a person has +ve blood type.

 

What is the probability that randomly chosen person has a -ve blood type?.

Explain your reasoning?.

Find the missing probability?.

 

 

 

 

 

 

 

 

 

 

 

A coin bank has 26 pennies, 15 nickels, 21 dimes and 16 quarters. When you pick the bank up, a single coin falls out.

Find the probability that a coin is:

  1. a penny b) a nickel c)a dime d)a quarter.

Find the probability that the coin is not a penny, dime, nickel or quarter.

Write a conjecture about the relationship between the probability that an event will occur and the probability that an event will not occur.

(The sum of the probability that an event will occur and the probability that an event will not occur is 1).

Review & Summary: Discussion of the important rules.

HW: Page 477 Q1 to 11.