37 lines
1.8 KiB
Markdown
37 lines
1.8 KiB
Markdown
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(Ch 13 14, stat 1040)
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Probability was developed to solve gambling problems. A chance can be represented as any of:
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- A percentage
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- A fraction
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- A decimal
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The chance of something gives is the likelihood of something happening when repeated under the same conditions. Chances are between 0 and 100%.
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The chance of something equals 100% - the probability of the opposite thing happening. This information is helpful when it's simpler to calculate the likelihood for the opposite of the desired probability.
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$$ chance = \frac{num\space outcomes}{num\space total\space possible\space outcomes} * 100\% $$
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Example: A coin toss has 2 possible outcomes, heads, and tails. $\{heads, tails\}$
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$p(h)$ is the mathematical shorthand for something happening, in this case $p(h)$ would be the probability of heads.
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- A deck of cards has 52 cards, 4 cards of each type and 13 different types.
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- The chance of drawing a specific card is 1/52
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- The chance of drawing a specific color is 1/2
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- The chance of drawing a specific type of a card is 4/52, or 1/13
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## Independent Events
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If the chance of a second event does not change depending on the outcome of the first event, an event is considered independent. An example of this might be drawing from a deck of cards, then replacing the card.
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To find the probability of two independent events taking place, you can multiply the probability of those events together.
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This is also known as unconditional chance.
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## Dependent Events
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If an event is influenced by other events, it is considered dependent. An example of this might be drawing from a deck of cards, not replacing, then drawing again.
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This is also known as conditional chance.
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| Phrase | Definition |
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| ---- | ---- |
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| Probability/Chance | The statistical likelihood of an event taking place |
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