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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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