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15.1 The probability that an outcome does not happen

15.1 The probability that an outcome does not happen

Here are some outcomes and their probabilities p.
1
Throwing a four with a dice: . It will rain tomorrow: 0.3. I shall win a game of chess: 90%.
6
The probability that an outcome does not happen = 1 – (probability that it does happen). (1 – p)
Here are the probabilities of the outcomes listed above not happening.
5
Not throwing a 4: . It will not rain tomorrow: 0.7. I shall not win the game: 10%.
6

Worked example 15.1
Jake estimates that the probability that his bus will be early is 0.05 and the probability that it will be
more than five minutes late is 0.3.
a What is the probability that it will not be early?
b What is the probability that it will not be more than 5 minutes late?

a 0.95 That is 1 – 0.95.
b 0.7 That is 1 – 0.3.

✦ Exercise 15.1

1 The probability that it will be warmer today than it was yesterday is 0.1.
The probability that it will be colder today than it was yesterday is 0.7.
a What is the probability that it will not be colder today than it was yesterday?
b What is the probability that it will not be warmer today than it was yesterday?
2 The table shows the age distribution of
Age Under 21 21 to 35 36 to 55 Over 55
members of a gym. A member of the
Percentage 12% 42% 32% 14%
gym is chosen at random. What is the
probability that the person is:
a 21 or more b 55 or less c not in the 21 to 35 age group?

3 The manager of a football team says the probability that the team win the next match is 0.6 and the
probability it will lose is 0.1.
Find the probability that the team will: a not win b not lose c not draw.

4 A survey of the makes of cars using a Make Volksota Toywagen Nindai Hyussan
particular road gave these results.
Percentage 12% 8% 7% 11%
a Harsha says that it must be wrong
because the probabilities do not add up to 100%. Explain why she is wrong.
b Find the probablity that the next car to use the road is:
i not a Toywagen ii not a Nindai iii not a Toywagen or a Nindai.
5 If you throw three dice, the probability of getting three sixes is 0.5%. The probability of getting no
sixes is 57.9%. Find the probability of getting:
a fewer than 3 sixes b at least one six.

15 Probability 149