Unit E: Statistics and Probability

Chapter 2: Probability

Calculating Probability

A high school football team is playing their championship game. The referee tosses a coin to see who has control of the ball first. There are two possible outcomes when flipping the coin: heads or tails. The captain of the white team called heads. A coin flip resulting in heads is a favourable outcome for the white team. However, heads would be an unfavourable outcome for the yellow team.

Probability is the mathematical term for the likelihood that something will occur. An outcome can be favourable or unfavourable. The formula for probability is

probability = \frac{number of favourable outcomes}{total number of possible outcomes}

Example 1

A coin is tossed.

What is the probability of tossing heads?
What is the probability of tossing tails?
Which outcome is more likely to occur when tossing a coin: heads or tails?

Solutions

$\begin{array}{rcl} probability & = & \frac{number of favourable outcomes}{total number of possible outcomes} \\ = & \frac{number of h e a d s on a coin}{total number sides on a coin} \\ = & \frac{1}{2} \\ = & 0.5 \end{array}$

The probability of heads is 0.5.
$\begin{array}{rcl} probability & = & \frac{number of favourable outcomes}{total number of possible outcomes} \\ = & \frac{number of t a i l s on a coin}{total number sides on a coin} \\ = & \frac{1}{2} \\ = & 0.5 \end{array}$

The probability of tails is 0.5.
The probability of tossing a coin is the same for both heads and tails.

Example 2

The following five coloured ducks are placed in a plastic bag. One duck is chosen.

What is the probability of choosing a green duck?
What is the probability of choosing a yellow duck?
Which outcome is more likely: choosing a green duck or choosing a yellow duck?

Solutions

$\begin{array}{rcl} probability & = & \frac{number of favourable outcomes}{total number of possible outcomes} \\ = & \frac{number of green ducks}{total number of ducks} \\ = & \frac{1}{5} \\ = & 0.2 \end{array}$

The probability of choosing a green duck is 0.2.
$\begin{array}{rcl} probability & = & \frac{number of favourable outcomes}{total number of possible outcomes} \\ = & \frac{number of yellow ducks}{total number of ducks} \\ = & \frac{4}{5} \\ = & 0.8 \end{array}$

The probability of choosing a yellow duck is 0.8.
It is more likely that a yellow duck will be chosen, since the probability of choosing a yellow duck is higher.

Example 3

In a pile of 35 buttons, there are 11 green buttons, 6 yellow buttons, 6 light blue buttons, and 12 dark blue buttons.

If one button is drawn randomly, what is the probability that the button will be green?
If one button is drawn randomly, what is the probability that the button will be green or yellow?

Solutions

$\begin{array}{rcl} probability & = & \frac{number of favourable outcomes}{total number of possible outcomes} \\ = & \frac{number of green buttons}{total number of buttons} \\ = & \frac{11}{35} \\ = & 0.314 \end{array}$

Note: If the probability results in a non-terminating decimal, record the probability to three decimal places.

The probability of drawing a green button is 0.314.
$\begin{array}{rcl} probability & = & \frac{number of favourable outcomes}{total number of possible outcomes} \\ = & \frac{number of green buttons + number of yellow buttons}{total number of buttons} \\ = & \frac{11 + 6}{35} \\ = & \frac{17}{35} \\ = & 0.486 \end{array}$

Note: The word or means the two values need to be added.

The probability of drawing a green or yellow button is 0.486.

Example 4

Nine red LEGO^® blocks are in a pile. One LEGO^® block is selected.

What is the probability of selecting a red LEGO^® block?
What is the probability of selecting a blue LEGO^® block?
Which outcome is more likely: selecting a red LEGO^® block or selecting a blue LEGO^® block?

Solutions

$\begin{array}{rcl} probability & = & \frac{number of favourable outcomes}{total number of possible outcomes} \\ = & \frac{number of red LEGO blocks}{total number of LEGO blocks} \\ = & \frac{9}{9} \\ = & 1 \end{array}$

The probability of selecting a red LEGO^® block is 1.
$\begin{array}{rcl} probability & = & \frac{number of favourable outcomes}{total number of possible outcomes} \\ = & \frac{number of blue LEGO blocks}{total number of LEGO blocks} \\ = & \frac{0}{9} \\ = & 0 \end{array}$

The probability of selecting a blue LEGO^® block is 0.
Selecting a red LEGO^® block is more likely since the probability is higher.

Important Notes about Probability:

A probability of 0 indicates that it is impossible for the outcome to occur.

A probability of 1 indicates that the outcome will definitely occur.

The probability value must be between 0 and 1.