Assessing risk in engineering, work and life

# Example 5 Combining two independent probabilities

When tossing a coin twice, what is the probability of getting heads both times?

Solution

Using the formula, the probability of each toss scoring a head is 1 in 2, 0.5 or , and the probability of scoring two heads is

0.5 × 0.5 = 0.25,

or

This can be checked by working from first principles. Tossing two coins (or one coin twice) gives the following four possible outcomes:

- heads, heads
- tails, tails
- heads, tails
- tails, heads.

From this, it can be seen that the probability of getting two heads is 1 in 4, , 0.25 or 25%.

## Activity 6 Combining probability

Allow approximately 20 minutes.

Calculate the probability of the following:

1. scoring two 6s by rolling two dice
2. scoring six 6s by rolling six dice.

Express your answers as both a fraction and a decimal (to 2 s.f.).

## Answer

1. The probability of scoring a 6 with one roll of a die is . For two dice, applying the formula gives an overall probability of

2. Similarly, for scoring six 6s, the overall probability is

Note that if you were to carry out these calculations using the rounded decimal value of 0.17 for the probability of a 6 (as calculated in Activity 5), you would have got the values 0.029 and 0.000 024, respectively. As this demonstrates, using rounded figures in calculations can have a significant effect.

OpenLearn - Assessing risk in engineering, work and life
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