3.8 Understanding the context and vocabulary of probability  (Page 2/4)

• We call the throwing of a dice (or a similar activity) an e x periment . The result when you throw the dice is called an outcome . If you are looking for, say, a three and you get a three, then this is called a successful outcome . With an ordinary dice, there are six possible outcomes . Now we can define the probability of something happening as:

$P=\frac{\text{number}\text{of}\text{successful}\text{outcomes}}{\text{number}\text{of}\text{possible}\text{outcomes}}$ .

ACTIVITY 2

To calculate probabilities in certain defined conte x ts

[LO 1.2, 1.4, 1.7, 5.4, 5.6]

Simple experiments

1 There are 12 balls in a bag: 3 blue balls, 5 green balls, 3 white balls and a red ball.

• If you take one out without looking, then the chance that it will be green is 5  12.
• It is correct to write this probability as: P = $\frac{5}{\text{12}}$ ; but it can also be written as a decimal fraction: P = 0,417. (Decimal fractions are often used as they make it easier to compare probabilities.)
• The probability of taking out a white ball is 0,25. What is the probability of taking out a ball that is either blue or white? P = $\frac{3+3}{\text{12}}=\frac{6}{\text{12}}=\frac{1}{2}=\mathrm{0,5}$ .

1.1 Calculate the probability of taking out a ball that is either green or blue.

1.2 What is the probability of taking out a yellow ball?

2 You throw an ordinary die. Calculate the probability of your throwing:

2.1 a two

2.2 an odd number

2.3 a number bigger than two.

Compound experiments.

3 Consider a coin that is tossed: it can land with either heads or tails up.

• The possibility of getting heads is exactly the same as getting tails, namely 0,5.
• But, if you toss a coin once and then once more, how likely is it that you will get two tails in a row?

First we have to find out what the total number of outcomes can possibly be. We could get (a) heads followed by heads, or (b) heads followed by tails; or we could get (c) tails followed by tails, or (d) tails followed by heads.

The total number of outcomes is four. Getting two tails in a row happens only once of the four outcomes. Therefore its probability is $\frac{1}{4}$ or 0,25.

A question for you:

3.1 How likely is it that you will toss two different sides of the coin in a row?

4 Take the bag of balls as another example:

• This time it has four balls – 1 each of red (R), green (G), blue (B) and yellow (Y).

• You draw a ball out, make a note of its colour and then put it back and draw again.
• An example: You draw red followed by yellow. This can be written as RY.

• If you do this, what is the likelihood that you will draw a blue ball both times?

• First determine the total number of outcomes:

• RR ; RG ; RB ; RY if the first ball was red.
• GR ; GG ; GB ; GY if the first ball was green.
• BR ; BG ; BB ; BY if the first ball was blue.
• YR ; YG ; YB ; YY if the first ball was yellow.

4.1 Draw the tree diagram for this problem.

• This shows that the total number of outcomes is 16! Of these outcomes, only one is BB, so our probability is 116 = 0,063. Calculate the probability that you will get

4.2 two balls of the same colour.

4.3 two balls of different colours.

4.4 at least one yellow ball.

4.5 a blue ball on the second draw.

4.6 a white ball.

4.7 no red balls.

ACTIVITY 3