
Outcomes,
Events and Probability
An outcome is something that may happen. A particular outcome is
spoken of as an event. The probability of an event is a measure
of how likely it is to happen. Sometimes this is judged from our
experiences over the years: e.g. "The probability of it raining
tomorrow is 50%".
Sometimes it is judged from the objects in front of us:
e.g. The probability of getting a head when a coin is flipped is
½.
The coin being flipped has only two outcomes, heads or tails. It
is assumed that these outcomes will occur equally often when the
coin is flipped.
Probability
of getting a head:
Number of outcomes resulting in head ÷ Total number of possible outcomes = ½
Judgements
can also be made about a fair dice because the outcomes are equally
likely.
Probability of getting a 3:
Number of outcomes resulting in 3 ÷ Number
of possible outcomes = 1/6
Probability
of getting an even number:
Number of times the event occurs ÷ Total
number of outcomes = 3/6 = 1/2
Changing the probability of an event
When a pack of playing cards is split, the probability of obtaining
an ace changes.
For the whole pack:
Probability of getting an ace = 4/52
= 1/13
For
the pack without the 12 picture cards (King, Queen, Jack):
Probability of getting an ace = 4/40
= 1/10
To
give a particular probability, the numbers of cards can be changed.
e.g. What cards could be used to make a probability of getting
an ace a 1/3?
There
are 4 aces, so the equivalent fraction 4/12
must be used instead of 1/3.
Eight
cards, which are not aces, can be placed with the 4 aces to give
the required probability.
Example:
A selection of cards has 3 aces and 4 non-aces. How many cards
must be added to this selection to make the probability of getting
an ace 1/3?
There are 3 aces and 7 cards altogether. An equivalent fraction
must be used with at least 3 aces and 7 cards.
The equivalent fractions are 1/3 = 2/6
= 3/9.
The
selection could be changed by adding two cards which are non-aces.
This would give:
Probability of getting an ace = 3/9= 1/3.
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