Example 4 Probability of scoring an even number
What is the probability of scoring an even number by rolling a die?
Solution
There are six possible outcomes from rolling a die, and three of them will give an even number (2, 4 and 6).
So the probability is 3 out of 6, which can be simplified to 1 out of 2.
This can be expressed as 1 in 2, , 0.5 or 50%.
Activity 5 Calculating probability
Timing: Allow approximately 20 minutes.
Calculate each of the following. Express your answers as a proportion, a fraction, a decimal and a percentage (to 2 s.f. where appropriate).
- a.The probability of scoring a 2 when rolling a die once.
- b.The probability of scoring higher than 2 when rolling a die once.
Answer
- a.There are six possible outcomes, and only one of these results in a 2. This means that the probability of rolling a 2 is 1 in 6, , 0.17 or 17%. (The probability of any one of the other numbers occurring is, of course, also 1 in 6.)
- b.The total number of outcomes is six, and four of these meet the condition of scoring higher than 2, so the probability is 4 out of 6 or 2 out of 3. This can be expressed as 2 in 3, two divided by three , 0.67 or 67%.