Key Stage 3

Data Handling Dimension

Learning Unit :Simple Idea of Probability

Learning Objectives :

• explore the meaning of probability through various activities

• have an intuitive idea about the relation between probability and the relative frequency as found in statistics or simulation activities

• investigate probability in real-life activities, including geometric probability

• compare the empirical and theoretical probabilities

• calculate the theoretical probability by listing the sample space and counting

Programme Title :Probability

Programme Objectives

  1. Understandintuitively that probability of an event is a number used to represent how much is its chance of happening.
  2. Recognize the fundamental formula of calculating the probability of an event, and realize that probability is a number between 0 and 1.
  3. Aware that in calculating probability, every possible outcome is equally likely.
  4. Recognize the use of tree diagram to identify the possible combinations of a compound event in order to calculate its probability.
  5. Understand the meaning of empirical (experimental) probabilities, and explore the relation between empirical (experimental) and theoretical probabilities.

Programme Content

Through the stories of some coincidences in daily life, it is pointed out that a small number is used to represent the very small chance of happening of an event and in mathematics, it is the probability of occurrence of the event.

The programme uses the different events of the game of tombola cage to introduce the fundamental formula of calculating probability. The cases of “a certain event” and “an impossible event” are explored and it is recognized that the range of probability lies between 0 and 1. The condition of equally likely for all possible outcomes of an event is stressed in the application of the formula.

A photograph of seven boys of a family brings forth the discussion of possible combinations of a family of seven children. A tree diagram is used for listing all combinations and the probability of having seven boys is calculated.

An experiment on throwing a die for a number of times is demonstrated to test the fairness of a die. Experimental(empirical) probability is thus introduced and it is shown that when the number of throws is large enough, the experiment probability approaches the theoretical probability.

Worksheet Answers

  1. For two people to be born on the same day of a year, one of them can be born on any day while the other must be born on that particular day. There is 365 days in a year, and the probability of the second people to be born on that particular day is then 1/365. Therefore, the probability of two people to be born on the same day of a year is 1/365.
  1. (a) The probabilities of getting a fruit for each of them are:

Smartie:36/200；Biggie：49/200；Wily：115/200.

(b) Expected number of fruits:

Smartie：72；Biggie：98；Wily：230.

  1. (a) The number of possible outcomes for drawing two green balls =9;

(b)Total number of possible outcomes =100;

(c) Probability of drawing two green balls =9/100=0.09

4. (a) 3/8; (b) 1/2

Key Stage 3 ETV Programme

《Probability》

Worksheet

  1. The birthday of the two American presidents, James K. Polk and Warren G. Harding, was on 2nd of November and their years of birth were not leap years.

James K. Polk Warren G. Harding

Two people are born on the same day of a year and their years of birth are not leap years. What is the probability of the occurrence of the incident?

  1. In the programme, Smartie,the smart clown, does an experiment to discover that the die used byWily, the crafty clown, is not a fair one. He throws the die 200 times and obtains the following results:

Number 1 2 3 4 5 6

Number 3 28 34 33 21 81

of throws

(a)The rules of the game are: When 1 or 4 is thrown, Smartie takes a fruit; when 2 or 5 is thrown, Biggie takes a fruit; when 3 or 6 is thrown, Wily takes a fruit. According to the results in the above table, what is the probability that each of them takes a fruit?

(b)There are 400 fruits on the trolley. If all of themare taken away by the three clowns in the game, what is the expected number of fruits taken by each of them?

  1. In the programme, there are 3 green balls(number 3, 4 and 8) out of 10 balls in the tombola cage. Two balls are drawn, the first ball is replaced before the second draw.

(a)How many different outcomes are there for drawing two green balls?

Useordered pairs to list out the outcomes:

Second green ball
No.3 No.4 No. 8
First green ball
No. 3
No. 4
No. 8 / (3,3) (3,4)

The total number of outcomes for two green balls:______

(b)What is the total number of outcomes for drawing two balls?

Similarly, use ordered pairs to list out all the possible outcomes:

(1,1)，(1,2)，(1,3)，……，(1,10)

(2,1)， (2,2)， (2,3)，……，(2,10)

(3,1)， (3,2)， (3,3)，……，(3,10)

………………………….

(10,1)，(10,2)，(10,3)，……，(10,10)

Therefore, the total number of possible outcomes is :______

(c)What is the probability of drawing two green balls?

Probability of drawing two green balls = / =______
  1. In the programme, the combinations of three children are listed:

According to the list, calculate:

(a)the probability that there is only one girl out of the three children;

(b)the probability that there is at least two girls out of the three children.

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