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16.1 Calculating probabilities

16.1 Calculating probabilities

When a football team play a match, they can win, draw or lose.

!ese are mutually exclusive outcomes. ! is means that if one outcome happens, the others cannot.

!ese three are all the possible outcomes. One of them must happen.

!e probabilities of all the mutually exclusive outcomes add up to 1.
Worked example 16.1

The probability that City will win its next football match is 0.65.
The probability City will draw is 0.2. Work out the probability that City will:
a not win b win or draw c lose.

a 1 – 0.65 = 0.35 If the probability of an outcome is p, the probability it will not occur is 1 – p.
b 0.65 + 0.2 = 0.85 The two outcomes are mutually exclusive so add the probabilities.
c 1 – (0.65 + 0.2) = 0.15 The probabilities for win, draw and lose add up to 1.

) Exercise 16.1

The probability that tomorrow’s
1 The temperature each day can be average, temperature will be average is 60%.
above average or below average.
Work out the probability that the The probability that the temperature
temperature will be: will be above average is 35%.
a below average b not above average c not below average.
not below average.
1
2 When Sasha throws two dice, the probability of her scoring two sixes is 36 . The probability of her
scoring one six is 5 .
18
Find the probability of Sasha scoring: a at least one six b no sixes.
1
3 Mia spins a coin until she gets a head. The probability she needs just one spin is . The probability
2
1
she needs two spins is 1 . The probability she needs three spins is . Work out the probability that
4
8
she needs:
a more than one spin b more than two spins c more than three spins.
4 This table shows the probability that a train will be late.
a Work out the missing probability.
b Find the probability that the train is: i not early ii not late.

Outcome Early On time Less than 5 minutes late At least 5 minutes late

Probability 0.10 0.74 0.12

5 A teacher is setting a test for the class next week. These are the probabilities for the day of the test.

Day Monday Tuesday Wednesday Thursday Friday

Probability 10% 20% 45% 15%

Work out the probability that the test will be on:
a Monday or Tuesday b Wednesday or Thursday c Friday.

152 16 Probability