MATHEMATICS FORM 4PROBABILITY I

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LEARNING OUTCOMES

At the end of the class, students should be able to:1.

2. 3. 4.

5.

Determine whether an outcomes is a possible outcome of an experiment. Determine the sample space of an experiment. Write the sample by using set notation. Identify the elements of a sample space which satisfy given condition. Find the ratio of the number of times an event occurs to the number of trials.MAIN MENU

PROBABILITY ISAMPLE SPACE EVENT PROBABILITY OF EVENT

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PROBABILITY I7.1 SAMPLE SPACE

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SAMPLE SPACE An

experiment is a process or an operation with an outcomes.

Toss a balanced die once and observe its uppermost face.TOPIC MENU

SAMPLE SPACE

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

Head Tail

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SAMPLE SPACE

The set of all possible outcomes of an experiment is called the sample space. It usually denoted by S. space Example 1: En. Adam has a fruit stall that sells bananas, apples, watermelons, papayas and durians. Students of class 4KP are asked to select their favorite fruit from the fruits at En. Adams stall. S = { banana, apple, watermelon, papaya, durian}

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SAMPLE SPACE Example

2:

A month is randomly selected from a year. Describe the sample space of this experiment by using set notation. S= { January, February, March, April, May, June, July, August, September, October, November, December}TOPIC MENU

PROBABILITY I7.2 EVENT

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EVENTIs a subset of the sample space. Is an outcome or a set of outcomes that satisfies certain condition. Denoted by a capital letter.

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EVENT

Example 1: A box contains five cards written with 1,2,3,4 and 5 respectively. A card is picked randomly from the box. S = {1, 2, 3, 4, 5}. If we define J as the card with an even number, the outcome of J in set notation will be J = { 2, 4 }.

J is known as an event of the experiment. The number of outcome of an event n(P)=2

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EVENT

Example 2: A letter is randomly selected from the word COMPUTER. Determine the number of possible outcomes of the event that the selected letter is i. A vowel ii. A consonant

vi.

Solution Let A = event that the selected letter is vowel = {O, U, E} Therefore n (A) = 3 Let B = event that the selected letter is consonant = {C, M, P, T, R} Therefore n (B) = 5TOPIC MENU

PROBABILITY I7.3 PROBABILITY OF AN EVENT

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PROBABILITY OF AN EVENT

Probability

of an event E,

P(E) = number of outcomes of the event number of outcomes of the sample space

P(E) = n (E) n (S) 0 P(E) 1TOPIC MENU

PROBABILITY OF AN EVENT P(E)

= 0 means that it is impossible for the event to happen. =1 means that the event is certain to happen. closer the probability of a given event is to 1, the more likely it is to happen.

P(E)

The

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PROBABILITY OF AN EVENT

Example A bag contains 3 red balls and 4 white ones. If Rashid puts his hand in the bag and picks a ball, what is the probability that the ball he picked is white?

Solution:

S = {R1,R2,R3,W1,W2,W3,W4} n(S)= 7 Let E is the event of drawing a white ball E = {W1,W2,W3,W4} n(E)=4 Therefore, the probability of drawing a white ball is 4 7TOPIC MENU

PROBABILITY ITUTORIAL

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EXERCISE 1

A number from 1 to 11 is chosen at random. What is the probability of choosing an odd number?A. B. C. D.

1/11 5/11 6/11 None of above

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EXERCISE 2

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. B. C. D.

(green, red) (green, green) (purple, purple) (white, white)

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EXERCISE 3

A dice is rolled 420 times. How many times will a number greater than 4 occur?A. B. C. D.

70 140 210 360

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EXERCISE 4

There are 45 boys and girls in a class. Given the probability that a boy is chosen is 4/15. the number of girls isA. B. C. D.

8 12 25 33

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EXERCISE 5

Out of 5000 applicants, only 275 are chosen. If Hazni is one of the applicants, what is the probability that he is chosen?A. B. C. D.

11/200 200/11 189/200 200/189

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