Probability

Understand Likelihood
and Probability

Mathematics 7

Common Core Volume 2: Pages 369 - 374

Shorouq Al Mamlakah International School

Saudi MOE LICENSE No. 520-3346

TAIF, K.S.A.

​

Lesson essential question:

Open Ended

What is probability?

Learning objective:

At the end of the session we are expected to:

✔

✔

Page 365

diagram

frequency

ratio

equivalent

Page 365

0.7

1

3

7

8

0.4

0.125

5

6

What is PROBABILTY?

Probability

is a measure of the likelihood of an

event to occur. Many events cannot be predicted

with total certainty.

Probability

provides information about the

likelihood that something will happen.

Meteorologists, for instance, use weather

patterns to predict the probability of rain. In

epidemiology, probability theory is used to

understand the relationship between exposures

and the risk of health effects.

Who is the father of probability?

Blaise Pascal

was a very influential French

mathematician and philosopher who contributed to

many areas of mathematics.

What is PROBABILTY?

The terms "likelihood" and "probability" refer to the likelihood

of events occurring.

Do you think it will be a fair decision?

There is a fight between two siblings over who gets to use the PlayStation first.
They decided to toss a coin to decide because they had been fighting for hours.

The oldest, Ameera, declared that she would play first if the coin landed heads up and that her sister Jana would play first if it landed heads down.

Open Ended

Can you suggest another possible way they could do to help them decide?

Possible outcomes:

Use the Probability to describe CHANCE

Alisa and Cheri spin the pointer and record the color that it lands on.

How can Alisa and Cheri explain their results?

1. The pointer will land at yellow.

The pointer should land on each color about 1 out of 4 times.

2. The pointer will land at green.

3. The pointer will land at blue.

4. The pointer will land at red.

Multiple Choice

If the first spinner shows a probability of pointing 1 color out of 4, or $$\frac{1}{4}$$ or 25%.
What do you think is the probability of the new spinner landing on a given color?

• $$\frac{1}{4}$$

• $$\frac{1}{8}$$

• $$\frac{2}{4}$$

• $$\frac{4}{8}$$

Outcome in Rolling a Dice

Use the probabilty and Likelihood to discribe a situation

Carrie will roll a number cube with sides label 1 to 6.

1, 2, 3, 4, 5, 6

What is the probability of rolling a number 2?

Outcome in Rolling a Dice

Use the probabilty and Likelihood to discribe a situation

Carrie will roll a number cube with sides label 1 to 6.

1, 2, 3, 4, 5, 6

What is the probability of rolling a number 2?

Use the probabilty and Likelihood to discribe a situation

Carrie will roll a number cube with sides label 1 to 6.

What is the probability of rolling a number 2?

What is the likelihood of rolling a 2?

Multiple Choice

In rolling a fair dice labeled with numbers 1 to 6.

What is the probability of rolling a number less than 7?

• $$\frac{1}{6}$$ or $$17\%$$

  It is unlikely to roll a number less than 7.

• $$\frac{3}{6}$$ or $$50\%$$

  There is an even chance to roll a number less than 7.

• $$\frac{6}{6}$$ or $$100\%$$

  It is certain to roll a number less than 7.

• $$\frac{0}{6}$$ or $$0\%$$

  It is impossible to roll a number less than 7.

Multiple Choice

In rolling a fair dice labeled with numbers 1 to 6.

What is the probability of rolling an even number?

• $$\frac{1}{6}$$ or $$17\%$$

  It is unlikely to roll an even number.

• $$\frac{3}{6}$$ or $$50\%$$

  There is an even chance to roll an even number.

• $$\frac{6}{6}$$ or $$100\%$$

  It is certain to roll an even number.

• $$\frac{0}{6}$$ or $$0\%$$

  It is impossible to roll an even number.

Multiple Choice

In rolling a fair dice labeled with numbers 1 to 6.

What is the probability of rolling a number greater than 6?

• $$\frac{1}{6}$$ or $$17\%$$

  It is unlikely to roll a number greater than 6.

• $$\frac{3}{6}$$ or $$50\%$$

  There is an even chance to roll a number greater than 6.

• $$\frac{6}{6}$$ or $$100\%$$

  It is certain to roll a number greater than 6.

• $$\frac{0}{6}$$ or $$0\%$$

  It is impossible to roll a number greater than 6.

What is the porbability of rolling an 11?

Use the probabilty and Likelihood to discribe a situation

The game piece shown has 12 sides, labeled 1 to 12.

What is the porbability of rolling an 11?

Use the probabilty and Likelihood to discribe a situation

The game piece shown has 12 sides, labeled 1 to 12.

1 out of 12

or 8.33%

It is unlikely to roll a number 11.

Multiple Choice

What is the probability of rolling a number greater than 5 in a 12 sided dice?

• $$\frac{7}{12}$$ or $$58.33\%$$

  It is likely to roll a number greater than 5.

• $$\frac{5}{12}$$ or $$41.67\%$$

  It is unlikely to roll a number greater then 5.

• $$\frac{12}{12}$$ or $$100\%$$

  It is certain to roll a number greater than 5.

• $$\frac{0}{6}$$ or $$0\%$$

  It is impossible to roll a number greater than 5.

Multiple Choice

What is the probability of rolling a number greater than 12 in a 12 sided dice?

• $$\frac{7}{12}$$ or $$58.33\%$$

  It is likely to roll a number greater than 12.

• $$\frac{5}{12}$$ or $$41.67\%$$

  It is unlikely to roll a number greater then 12.

• $$\frac{12}{12}$$ or $$100\%$$

  It is certain to roll a number greater than 12.

• $$\frac{0}{12}$$ or $$0\%$$

  It is impossible to roll a number greater than 12.

Using Probability to Examine Fairness

Marie designed a spinner for a game. The spinner is considered fair if there is an equal chance for the pointer to land in each letter.
The design of the spinner is shown below, is the spinner a fair spinner?

Using Probability to Examine Fairness

Marie designed a spinner for a game. The spinner is considered fair if there is an equal chance for the pointer to land in each letter.
The design of the spinner is shown below, is the spinner a fair spinner?

It is more likely that the spinner will land on A than any other letter.

The spinner is not fair.

Poll

Is the spinner shown a fair spinner?

• Yes, it is a fair spinner

• No, it is not a fair spinner.

Open Ended

Can you suggest possible ways to make the spinner fair?

Take note!

1.

What is probability?

Probability describes the likelihood that a chance event will occur.

2.

How can you use probability to draw conclusions about the likelihood
that something will occur?

The higher the probability of something, the more likely it will occur.

3.

Why is probability limited to number between 0 and 1?

Probability is shown using a ratio of the number of favorable

outcomes to the total number of possible outcomes.

The number of favorable outcomes could be the same as, but not

greater than, the total number of possible outcomes, so the probability

would be

1

.

Fill in the Blank

Allie is going to select a card from the group of cards shown.

The probability that Allie will select a card labeled 3 is ___ out of 10 or 20 %.

Fill in the Blank

Allie is going to select a card from the group of cards shown.

Because the probability that each number will be selected is not equal, the group of cards is ___________.

Fill in the Blank

Allie is going to select a card from the group of cards shown.

It is _________ that Allie will select a card labeled with a number less than 6.

Fill in the Blank

Allie is going to select a card from the group of cards shown.

It is _________ that Allie will select a card labeled 4.

Open Ended

Exit Tickets.

What is probability and how it is related to outcomes?

Homework

Answer PRACTICE & PROBLEM SOLVING
On page 373 of your vol. 2 book

6

3

75

likely

0

impossible

2

7

2

7

unlikely

The second bag,

3

20

=

15

100

= 15%

and

170

500

=

34

100

= 34%.

So it is more likely to pick a tile

that is labeled Y from the second bag.

If a tile is selected and then replaced before

selecting the next tile, and 100 tiles are selected

this way, you can expect to draw about 34

tiles labeled Y in the second bag, compared to

15 tiles labeled Y in the first bag.

The probability is

20

40

, or

1

2

.

This means the likelihood of choosing

a white marble can be described as

neither likely nor unlikely, but there

is an even chance.