Probability - Long term proportion of times an outcome occurs; never interested in short term outcomes.
Sample Space - List of all possible outcomes
Coin example
Applying the logic of the coin toss to our ROYP balls, if 1 = Red, 2 = Orange, 3 = Yellow, 4 = Purple
1234 2134 3124 4123
1243 2143 3142 4132
1324 2314 3214 4213
1342 2341 3241 4231
1423 2413 3412 4312
1432 2431 3421 4321
How many chances to have none of the numbers in the right order?
1234 2134 3124 4123
1243 2143 3142 4132
1324 2314 3214 4213
1342 2341 3241 4231
1423 2413 3412 4312
1432 2431 3421 4321
9/24 = 37.5%
How many chances to have 1 number in the right order?
1234 2134 3124 4123
1243 2143 3142 4132
1324 2314 3214 4213
1342 2341 3241 4231
1423 2413 3412 4312
1432 2431 3421 4321
8/24 = 33.3%
How many chances to have 2 numbers in the right order?
1234 2134 3124 4123
1243 2143 3142 4132
1324 2314 3214 4213
1342 2341 3241 4231
1423 2413 3412 4312
1432 2431 3421 4321
6/24 = 25%
How many chances to have 3 numbers in the right order?
1234 2134 3124 4123
1243 2143 3142 4132
1324 2314 3214 4213
1342 2341 3241 4231
1423 2413 3412 4312
1432 2431 3421 4321
0/24 = 0%
How many chances to have all 4 numbers in the right order?
1234 2134 3124 4123
1243 2143 3142 4132
1324 2314 3214 4213
1342 2341 3241 4231
1423 2413 3412 4312
1432 2431 3421 4321
1/24 = 4.167%
Examples on page 207 of Discovering Statistics
Applying the logic to a deck of cards...
What's probability of getting an ace? [p(ace)]=4/52 or 7.69%
What's probability of getting a red card? [p(red)]=26/52 or 50.0%
What's probability of getting a red king? [p(red king)]=2/52 or 3.85%
Probability of rolling a 2 on a fair die?[p(die 2)] = 1/6 or 16.67%
Probability of rolling a 2 on two fair dice?[p(die 2)] = 1/36 or 2.78%
Probability of rolling a sum of 3 on two fair dice?[p(sum 3)] = 2/36 or 5.56%
Probability of rolling a sum of 7 on two fair dice?[p(sum 3)] = 6/36 or 16.67%
If you are unclear on any of this, please watch this video.
Lotto example.
Rules: Pick 5 numbers between 1 and 56, with no repetition. The mega number must be between 1 and 46.
Visually represented:
56 * 55 * 54 * 53 *52 = 458,377,920
458,377,920 * 46 = 2.108538432x1010
Unfortunately, these values account for a lot of repetition in the pattern sequence
The actual probability is 175,711,536. How do we eliminate the repetition?
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