Copyright©Ed2NetLearning.Inc 1 OUTCOMES. Copyright©Ed2NetLearning.Inc 2 Previous Knowledge 1. A...

Copyright©Ed2NetLearning.Inc 1

OUTCOMES


Previous Knowledge

1. A number cube is rolled. What is the probability of rolling a composite number? Answer: 1/3

2. List all the outcomes for the following experiments>a. tossing a coin – head & tailb. rolling a number cube – 1, 2, 3, 4, 5, 6c. choosing a color of the American flag

- red, white, blue.


OUTCOMES- OBJECTIVES

1. To understand sample space

2. To find the outcomes using lists and tree diagrams.


SAMPLE SPACE - DEFINITION

The set of all possible outcomes is called the sample space.

Example: The sample space for rolling a cube is listed as { 1, 2, 3, 4, 5, 6} There are 6 possibilities.A tree diagram can also be used to show a sample space.A tree diagram is a diagram that shows all possible outcomes of an event.


Sample Space

Q Take 2 dice and throw them together. The possible outcomes are:

A { (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}

The set of all outcomes is a sample space. The above example is a sample space. There are 36 possibilities.


Now your turn

QTake 2 coins and toss them. Write the sample space?

A { (H,H) (H,T) (T,H) (T,T)}


FIND A SAMPLE SPACE

Q.How many outfits are possible from a choice of blue or black shorts and a choice of yellow, orange or red shirt?

A. Shorts Shirt Outcome

blue(B)

White(w)

there are 6 possible outfits.

Yellow (y)

Orange (o)Red (r) Yellow(Y) Orange(o) Red (r )

BYBOBR

WYWOWR


Now your turn

A car can be purchased with two doors and four doors. You can also choose leather, fabric or cushion seats. Draw a tree diagram.

2 doors (2)

4 doors(4)

Leather(l)

Fabric(f)

Cushion(c )

Leather(L)

Fabric(F)

Cushion(C )

2L

2F

2C

4L

4F

4C


Find Probability

When you know the number of outcomes, we can easily find the probability that an event can occur.

Probability = Number of ways an event can happen

Total number of possible outcomes


Find probability

Q. Two coins are thrown. What is the probability that both are heads?

First write the sample space. (H,H) (H,T) (T,H) (T,T) There are 4 possibilities Probability of both showing head is (H,H)

That is only 1 possibility Probability = ¼


Now Your Turn

Q. Two dice are thrown. i) What is the probability that both dice showing 1?

ii) what is the probability that both showing the same number?

A. i) Total number of outcomes = 36

Number of possible ways in which both dice showing 1 = 1

Probability = 1 36

ii) Total number of outcomes =36Number of possibilities in which both dice showing the same number = 6 {(1,1) (2,2) (3,3) (4,4) (5,5) (6,6)}

Probability = 6 36


Use Tree Diagram To Find Probability

Q. Max spins two spinners. What is the probability of spinning yellow on the first spinner and red on the second spinner?

Spinner 1 Spinner 2 R Y R Y

Yellow(Y)

Red(R)

One outcome has yellow and then red. There are 4 possible outcomes. So P(yellow, red) = ¼

YELLOW(y)

RED(r )

YELLOW (y)

RED ( R )

YY

YR

RY

RR


Another example to find probability from a tree diagram

Q. A penny is tossed and a number cube is rolled. Use a tree diagram to find the probability of getting a head and a 5.

Penny Number cube Outcome 1 H1

Heads(H) 2 H23 H34 H45 H56 H6

Tails(T) 1 T12 T23 T34 T4 5 T56 T6

Total outcomes = 12

So, P(head,5) = 1 12


Now Your Turn

Chocolate, vanilla, strawberry icecreams with sugar or waffle cone. How many outcomes are possible? Find P (chocolate,sugar) ?

chocolate

vanilla

strawberry

There are 6 outcomes. P (chocolate,sugar) = 1/6

Sugar

Waffle cone

Sugar

Waffle cone

Sugar

Waffle cone

Chocolate,sugar

Chocolate, waffle cone

Vanilla sugar

Vanilla waffle cone

Strawberry sugar

Strawberry waffle cone


Review

1. To understand sample space

2. To find the outcomes using lists and tree diagrams.

3. To find the probability using tree diagram


Assessment

1. From a group of 2 men and 3 women two persons are selected. Describe the sample space of the experiment.

Let M1, M2, W1, W2, W3 represents men and women in the group.

sample space = { M1M2, M1W1, M1W2, M1W3, M2W1, M2W2, M2W3, W1W2, W1W3, W2W3 }

2. Two dice are thrown simultaneously. Find the probability of getting a multiple of 3 as the sum? 1

3


Assessment

3. A bag contains 5 white, 7 black and 8 red balls. A ball is chosen at random. What is the probability that it is a red ball or a white ball?total number of balls = 5+7+8 = 20P (ball is red or white) = 8 + 5 = 13

20 204. Three coins are tossed. Find the probability of getting

atleast two heads? ½ 5. A coin is tossed. If it shows head, we draw a ball from a

bag containing 3 red and 4 black balls. Write the sample space ? { HR1, HR2, HR3, HB1, HB2, HB3 and HB4}


Assessment

6. In a single throw of 3 dice, find the probability of getting a total less than 5?Sample space = { (1,1,1) ,(1,1,2), ……,(6,6,6)}number of possible outcomes = 6 x 6 x 6 = 216Possible outcomes = (1,1,1), (1,1,2) (1,2,1), (2,1,1) = 4 P (total less than 5) = 4 = 1

216 54 7. An urn contains 8 red, 3 white and 9 blue balls. If 1

balls is chosen at random. Determine the probability that the ball is red? 8

20


Assessment

8. From a bag containing 5 red and 4 black balls, a ball is drawn at random. What is the probability that it is a black ball? 4

9 9. Find the probability of getting a ‘king’ or a ‘queen’ in a

single draw from a well shuffled pack of playing cards? 2

13 10. A family has 2 boys and 3 girls. Two persons are

selected. Write down the sample space of this experiment. { G1G2,G1G3,G2G3, G1B1, G1B2, G2B1, G2B2, G3B1, G3B2, B1B2 }


Great Job!

Copyright©Ed2NetLearning.Inc 1 OUTCOMES. Copyright©Ed2NetLearning.Inc 2 Previous Knowledge 1. A...

Documents

Transcript of Copyright©Ed2NetLearning.Inc 1 OUTCOMES. Copyright©Ed2NetLearning.Inc 2 Previous Knowledge 1. A...