SOCR EduMaterials Activities Discrete Probability examples
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* '''Description''': You can access the applets for the distributions at http://www.socr.ucla.edu/htmls/SOCR_Distributions.html . | * '''Description''': You can access the applets for the distributions at http://www.socr.ucla.edu/htmls/SOCR_Distributions.html . | ||
* '''Example 1:''' | * '''Example 1:''' | ||
- | Find the probability that 3 out of 8 plants will survive a frost, given that any such plant will survive a frost with | + | Find the probability that 3 out of 8 plants will survive a frost, given that any such plant will survive a frost with probability of 0.30. Also, find the probability that at least 1 out of 8 will survive a frost. What is the expected value and standard deviation of the number of plants that survive the frost? |
* '''Answer:''' | * '''Answer:''' | ||
*<math> X \sim b(8,0.3) </math>, <math> P(X=3)= {8 \choose 3} 0.3^30.7^5=0.2541</math> | *<math> X \sim b(8,0.3) </math>, <math> P(X=3)= {8 \choose 3} 0.3^30.7^5=0.2541</math> |
Revision as of 19:47, 24 April 2007
- Description: You can access the applets for the distributions at http://www.socr.ucla.edu/htmls/SOCR_Distributions.html .
- Example 1:
Find the probability that 3 out of 8 plants will survive a frost, given that any such plant will survive a frost with probability of 0.30. Also, find the probability that at least 1 out of 8 will survive a frost. What is the expected value and standard deviation of the number of plants that survive the frost?
- Answer:
- ,
Below you can see a SOCR snapshot for this example:
- Example 2:
If the probabilities of having a male or female offspring are both 0.50, find the probability that a familiy's fifth child is their first son.
- Answer:
- 0.505
- Example 3:
- a. ,
- b. ++
- Example 4:
- 0.740.3
- Example 5:
- Example 6:
- a. ,
- b. P(X = 0) = 1 − 0.999 = .001
0.001 = 0.1n n = 3