## Notes on Probability

What is probability?
Probability is the likelihood of something happening in the future.

How is it expressed?

Probability is expressed as a fraction: the denominator is the total number of ways things can occur and the numerator is the number of things that you are hoping will occur:
```
NUMBER OF THINGS YOU ARE LOOKING FOR
PROBABILITY = ---------------------------------------
TOTAL NUMBER OF THINGS
```

Example ProblemAnswer
1What is the probability of
a flipped coin turning up heads?
because there is 1 head and the coin has 2 sides.

2What is the probability of pulling,
at random, the ace of spades
out of a deck of 52 cards?
because there is only 1 ace of spades and there are 52 cards in the deck.
3What is the probability of drawing
any ace out of a deck of 52 cards?
because there 4 aces in a deck of 52 cards.
4What is the probability of drawing a red marble out of a bag containing 2 red marbles and 5 blue marbles?
 because there are 2 red marbles and 7 marbles in all.

Remember, probability is not dependent on what has happened in the past. So if you have tossed a coin and it has come up heads 6 times in a row, the probability of it coming up heads a 7th time is still