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Assessing risk in engineering, work and life
Assessing risk in engineering, work and life

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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, one divided by two, 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, one divided by six , 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 threetwo divided by three , 0.67 or 67%.