mat f4 probability 1

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MATHEMATICS FORM 4

PROBABILITY IPROBABILITY I


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LEARNING OUTCOMESLEARNING OUTCOMES

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LEARNING OUTCOMESLEARNING OUTCOMES

At the end of the class, students should be

able to:

1. Determine whether an outcomes is a possible

outcome of an experiment.2. Determine the sample space of an experiment.

3. Write the sample by using set notation.

4. Identify the elements of a sample space which satisfy

given condition.5. Find the ratio of the number of times an event occurs

to the number of trials.

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EVENTEVENT

SAMPLE SPACESAMPLE SPACE

PROBABILITY OF EVENTPROBABILITY OF EVENT

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7.1 SAMPLE SPACE7.1 SAMPLE SPACE

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An experimentexperiment is a process or anoperation with an outcomes.

Toss a balanced die once and observe itsuppermost face.



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When toss the coin, we can get only 2results:

1.1. HeadHead

2.2. TailTail



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The set of all possible outcomes of an experiment iscalled the sample spacesample space. It usually denoted by SS.

Example 1:

En. Adam has a fruit stall that sells bananas, apples,watermelons, papayas and durians. Students ofclass 4KP are asked to select their favorite fruit from

the fruits at En. Adams stall.

SS = { banana, apple, watermelon, papaya, durian}



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Example 2:

A month is randomly selected from a year.

Describe the sample space of thisexperiment by using set notation.

SS= { January, February, March, April,May, June, July, August, September,October, November, December}



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7.2 EVENT7.2 EVENT



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EVENTEVENT

Is a subset of the sample space.

Is an outcome or a set of outcomesthat satisfies certain condition.

Denoted by a capital letter.



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EVENTEVENT

Example 1:

A box contains five cards writtenwith 1,2,3,4 and 5 respectively. Acard is picked randomly from thebox.

S ={1, 2, 3, 4, 5}.

If we define J as the card withJ as the card withan even numberan even number,, the outcomeof J in set notation will be

J = { 2, 4 }.J = { 2, 4 }.

J is knownas an eventof theexperiment.

The numberof outcomeof an eventn(P)=2



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EVENTEVENT

Example 2:

A letter is randomly selected from the word COMPUTER.Determine the number of possible outcomes of the eventthat the selected letter is

i. A vowel

ii. A consonant

SolutionSolution

i. Let A = event that the selected letter is vowel = {O, U, E}

Therefore n (A) = 3

ii. Let B = event that the selected letter is consonant = {C, M,P, T, R} Therefore n (B) = 5



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7.3 PROBABILITY OF AN7.3 PROBABILITY OF AN

EVENTEVENT



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PROBABILITY OF AN EVENTPROBABILITY OF AN EVENT

Probability of an event E,

P(E) = number of outcomes of the eventP(E) = number of outcomes of the eventnumber of outcomes of thenumber of outcomes of thesample spacesample space

P(E) = n (E)P(E) = n (E)

n (S)n (S)

0 P(E) 10 P(E) 1



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P(E) = 0P(E) = 0 means that it is impossible forthe event to happen.

P(E) =1P(E) =1 means that the event is certainto happen.

The closer the probability of a given eventis to 1, the more likely it is to happen.



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ExampleExample

A bag contains 3 red balls and 4 white ones. If Rashid putshis hand in the bag and picks a ball, what is the probabilitythat the ball he picked is white?

Solution:Solution:

S = {R1,R2,R3,W1,W2,W3,W4}n(S)= 7

Let E is the event of drawing a white ballE = {W1,W2,W3,W4}n(E)=4

Therefore, the probability of drawing a white ball is 4

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EXERCISE 1EXERCISE 1

A number from 1 to 11 is chosen at

random. What is the probability of

choosing an odd number?

A. 1/11

B. 5/11

C. 6/11

D. None of above

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A bag consists of 3 green, 1 white and 1

purple chips. Two chips are drawn from

the bag. Which of the following outcomes

are possible?

A. (green, red)

B. (green, green)

C. (purple, purple)

D. (white, white)

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A dice is rolled 420 times. How many

times will a number greater than 4

occur?

A. 70

B. 140

C. 210

D. 360

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There are 45 boys and girls in a class.

Given the probability that a boy is

chosen is 4/15. the number of girls is

A. 8

B. 12

C. 25

D. 33

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Out of 5000 applicants, only 275 are

chosen. If Hazni is one of the applicants,

what is the probability that he is chosen?

A. 11/200

B. 200/11

C. 189/200

D. 200/189

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The answer is incorrect.The answer is incorrect.

Please try again.Please try again.


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Congratulation!!!Congratulation!!!

The answer is correctThe answer is correct

mat f4 probability 1

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