'Random' and 'randomly'

In probability, we frequently hear the words 'chosen randomly' or 'chosen at random'.

For example:

• A student was chosen at random to answer a question.
• I set the playlist on my iPod to random.
• The winning numbers in the lottery draw roll randomly out of the barrel.

These are all instances where each element in the list, or sample space – the students in the class, the songs on the iPod, the numbers in the lottery barrel – all have an equally likely chance of being selected. They are examples of experiments where all the possible outcomes are equally likely, just like tossing the die.

Example 5

There are three green apples and four red apples in a bowl. Michael is blindfolded and randomly chooses an apple. What is the probability that he selects a green apple?

Solution

There are seven apples in the bowl and three are green.

P(apple is green) = \(\dfrac{3}{7}\)

Example 6

The letters of the word 'MELBOURNE' are written on pieces of paper and placed in a box. Janine randomly selects one piece of paper from the box and records the letter written on the paper. What is the probability of Janine choosing:

1. the L?
2. an E?
3. a vowel?

Solution

The number of letters in the sample space = 9.

1. There is one L.
   P(letter is L) = \(\dfrac{1}{9}\)
2. There are two Es.
   P(letter is E) = \(\dfrac{2}{9}\)
3. There are four vowels.
   Vowels: E O U E
   P(letter is a vowel) = \(\dfrac{4}{9}\)