SOCR EduMaterials Activities Discrete Probability examples
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* '''Example 6:''' | * '''Example 6:''' | ||
**a. <math>X \sim b(5,0.90). P(X=4)= {5 \choose 4} 0.9^4 0.1^1=0.32805</math> | **a. <math>X \sim b(5,0.90). P(X=4)= {5 \choose 4} 0.9^4 0.1^1=0.32805</math> | ||
+ | <center>[[Image: SOCR_Activities_Binomial_Christou_example6_1st.jpg|600px]]</center> | ||
**<math>P(X\ge 1)= 1-P(X=0)= 1- 0.1^4=0.9999</math> | **<math>P(X\ge 1)= 1-P(X=0)= 1- 0.1^4=0.9999</math> | ||
+ | <center>[[Image: SOCR_Activities_Binomial_Christou_example6_2nd.jpg|600px]]</center> | ||
**b. <math>P(X=0)=.001, | **b. <math>P(X=0)=.001, | ||
0.001= 0.1^n | 0.001= 0.1^n | ||
n= 3</math> | n= 3</math> | ||
- | <center>[[Image: | + | <center>[[Image: SOCR_Activities_Binomial_Christou_example6_b.jpg|600px]]</center> |
* '''Example 7:''' | * '''Example 7:''' |
Revision as of 02:19, 25 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 SOCR snapshots 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:
- Example 6:
- a.
- b. P(X = 0) = .001,0.001 = 0.1nn = 3
- Example 7: