3.8 Understanding the context and vocabulary of probability

Mathematics

Grade 9

Number patterns

Graphical representations

Equations statistics

Probability theory

Module 20

Understanding the context and vocabulary of probability

What is gambling all about?

ACTIVITY 1

To understand the context and vocabulary of probability

[LO 11.2, 5.1, 5.6]

1 The following very ordinary statements all deal with probability – but they are not all perfectly accurate. With your partner, study them and decide what is left unsaid, or what information you need to be able to evaluate them. Write down the results of your discussion.

For example : “The sun will come up tomorrow morning” really means: “If I go by the fact that the sun has come up every morning of my life, I am very certain that it will happen again tomorrow morning.”

1.1 If I toss a coin, there is a 50:50 chance that it will land tails up.

1.2 Kevin is certain to phone me tonight.

1.3 It is virtually impossible to win the lottery.

1.4 If you have a positive HIV test, then you will die of AIDS.

1.5 You are more likely to die of a spider-bite than of a lightning strike.

1.6 If you are told that every raffle ticket has two numbers, you have a double chance to win.

1.7 If you don’t play the Lotto, you are certain not to win.

1.8 In a room of 24 people, you are likely to find two people with the same birthday.

1.9 There is a 25% chance of rain tomorrow.

1.10 You are as likely to get a three as a four when you throw a die.

• Check the quality of your answers:

2 Refer to the following scale

• The likelihood of something happening must lie somewhere along this line of probabilities. Nothing can be less likely than 0%, and nothing can be more likely than 100%. If you throw an ordinary six-sided die, then it is certain (meaning 100% on the above scale) that the number it shows will be either 1, 2, 3, 4, 5 or 6. It is impossible (0%) that it will show a 7. We can’t always be sure exactly where a certain probability lies, but in some cases the probability can be worked out exactly.

• Write down at which percentage of the scale above each of the following statements falls; afterwards discuss your answers with your partner.

2.1 I will throw a six with an ordinary die.

2.2 If you pick a Smartie with your eyes closed, it will be a red one.

2.3 I will visit a friend next weekend.

2.4 The numbers 1, 2, 3, 4, 5 and 6 are equally likely from throwing a die.

2.5 I will meet the president of South Africa someday.

2.6 I will stay the same height for the next year.

2.7 I will get a cold next winter.

2.8 I will be the president of South Africa someday.

• How was the quality of my work now?

• Here is the same scale with other values:

• These same probabilities are often written as a simplified fraction. Note that the line goes from 0 (impossible) to 1 (certain). We can’t have probabilities that are greater than 1 – nothing can be more likely than absolutely certain! In other words, these probabilities can’t be fractions with a larger numerator than denominator.

• Let’s look at the die again to make it clear how it works. The dice can show one of six numbers, but the chance that it will be a six is only one out of six chances. Look at it this way: if six friends throw one dice, and each chooses a different number from 1 to 6, then it is certain that one will be right! So, each of them has only 1 of the 6 chances to be right. The fraction (the probability) is $\frac{1}{6}$ , which lies between 10% and 20% on the scale.