Probability
Probability is about how Likely something is to occur, or how likely something is true.
The mathematic probability is a Number between 0 and 1.
0 indicates Impossibility and 1 indicates Certainty.
The Probability of an Event
The probability of an event is:
The number of ways the event can happen / The number of possible outcomes.
Probability = # of Ways / Outcomes
Tossing Coins
When tossing a coin, there are two possible outcomes:
| Way | Probability |
|---|---|
| Heads | 1/2 = 0.5 |
| Tails | 1/2 = 0.5 |
P(A) - The Probability
The probability of an event A is often written as P(A).
When tossing two coins, there are 4 possible outcomes:
| Event | P(A) |
|---|---|
| Heads + Heads | 1/4 = 0.25 |
| Tails + Tails | 1/4 = 0.25 |
| Heads + Tails | 1/4 = 0.25 |
| Tails + Heads | 1/4 = 0.25 |
Throwing Dices
When throwing a dice, there are 6 possible outcomes:
| Event | P(A) |
|---|---|
| Lands on 1 | 1/6 = 0.166666 |
| Lands on 2 | 1/6 = 0.166666 |
| Lands on 3 | 1/6 = 0.166666 |
| Lands on 4 | 1/6 = 0.166666 |
| Lands on 5 | 1/6 = 0.166666 |
| Lands on 6 | 1/6 = 0.166666 |
The possibility of throwing 3 fours at the same time is
(1/6)3 (Lands on 4 to the power of 3):
The possibility of throwing 3 likes at the same time is 6 times larger:
(lands on 1) + (Lands on 2) + ... + (Lands on 6)
6 Balls
I have 6 balls in a bag: 3 reds, 2 are green, and 1 is blue.
Blindfolded. What is the probability that I pick a green one?
Number of Ways it can happen are 2 (there are 2 greens).
Number of Outcomes are 6 (there are 6 balls).
Probability = Ways / Outcomes
The probability that I pick a green one is 2 out of 6: 2/6 = 0.333333.
The probability is written P(green) = 0.333333.
| P(A) | W/O | Probability |
|---|---|---|
| P(red) | 3/6 | 0.5000000 |
| P(green) | 2/6 | 0.3333333 |
| P(blue) | 1/6 | 0.1666666 |
P(A) = P(B)
| P(A) = P(B) | Event A and B have the same chance to occur |
| P(A) > P(B) | Event A has a higher chance to occur |
| P(A) < P(B) | Event A has a lower chance to occur |
For the 6 balls:
| P(red) > P(green) | I am more likely to pick a red than a green |
| P(red) > P(blue) | I am more likely to pick a red than a blue |
| P(green) > P(blue) | I am more likely to pick a green than a blue |
| P(blue) < P(green) | I am less likely to pick a blue than a green |
| P(blue) < P(red) | I am less likely to pick a blue than a red |
| P(green) < P(red) | I am less likely to pick a green than a red |
Choosing a King
The probability of choosing a king in a deck of cards is 4 in 52.
Number of Ways it can happen are 4 (there are 4 kings).
Number of Outcomes are 52 (there are 52 cards).
Probability = Ways / Outcomes
The probability is 4 out of 52: 4/52 = 0.076923.
The probability is written P(king) = 0.076923.
