Wednesday, March 28, 2012

03-28-2012

In Class ROYP Ball Exercise

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?

No comments:

Post a Comment