SOCR EduMaterials Activities Discrete Probability examples
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* <math>P(X=5)=0.7^4 0.3=0.07203,</math>where X represents the number of trials. | * <math>P(X=5)=0.7^4 0.3=0.07203,</math>where X represents the number of trials. | ||
* '''Example 5:''' | * '''Example 5:''' | ||
- | <math> E(X)=\frac{1}{0.30}=3.33</math> | + | <math> E(X)=\facr{1}{p}=\frac{1}{0.30}=3.33</math> |
* '''Example 6:''' | * '''Example 6:''' | ||
- | **a. <math>X \sim b(5,0.90) | + | **a. <math>X \sim b(5,0.90). P(X=4)= {5 \choose 4} 0.9^4 0.1^1=0.32805</math> |
- | **<math>P(X\ge 1)= 1-P(X=0)= 1- 0.1^4 </math> | + | **<math>P(X\ge 1)= 1-P(X=0)= 1- 0.1^4=0.9999</math> |
- | **b. <math>P(X=0) | + | **b. <math>P(X=0)=.001, |
- | + | 0.001= 0.1^n</math> <math>n= 3</math> |
Revision as of 20:01, 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:
- P(X = 5) = 0.505 = 0.03125
- Example 3:
- a. ,
- b.
- Example 4:
- P(X = 5) = 0.740.3 = 0.07203,where X represents the number of trials.
- Example 5:
Failed to parse (unknown function\facr): E(X)=\facr{1}{p}=\frac{1}{0.30}=3.33
- Example 6:
- a.
- b. P(X = 0) = .001,0.001 = 0.1n n = 3