SOCR EduMaterials Activities Discrete Probability examples
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0.001= 0.1^n | 0.001= 0.1^n | ||
n= 3.</math> | n= 3.</math> | ||
- | *In the first snapshot below, <math>n=2, | + | *In the first snapshot below, where<math>n=2, P(X\ge1)=0.99,</math> which is too small. In the second snapshot, we can see that when n is increased to 3, <math>P(X\ge1)</math> increases to nearly 1. </math> |
<center>[[Image: SOCR_Activities_Binomial_Christou_example6_b_n=2.jpg|600px]]</center> | <center>[[Image: SOCR_Activities_Binomial_Christou_example6_b_n=2.jpg|600px]]</center> | ||
<center>[[Image: SOCR_Activities_Binomial_Christou_example6_b_n=3.jpg|600px]]</center> | <center>[[Image: SOCR_Activities_Binomial_Christou_example6_b_n=3.jpg|600px]]</center> | ||
* '''Example 7:''' | * '''Example 7:''' |
Revision as of 15:38, 26 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:
![](/socr/uploads/thumb/e/e2/SOCR_Activities_Binomial_Christou_example1.jpg/600px-SOCR_Activities_Binomial_Christou_example1.jpg)
![](/socr/uploads/thumb/f/fa/SOCR_Activities_Binomial_Christou_example1_2nd.jpg/600px-SOCR_Activities_Binomial_Christou_example1_2nd.jpg)
- 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
![](/socr/uploads/thumb/d/da/SOCR_Activities_Binomial_Christou_example2.jpg/600px-SOCR_Activities_Binomial_Christou_example2.jpg)
- Example 3:
- a.
,
- a.
![](/socr/uploads/thumb/0/00/SOCR_Activities_Binomial_Christou_example3.jpg/600px-SOCR_Activities_Binomial_Christou_example3.jpg)
- b.
- b.
![](/socr/uploads/thumb/7/72/SOCR_Activities_Binomial_Christou_example3_2nd.jpg/600px-SOCR_Activities_Binomial_Christou_example3_2nd.jpg)
- Example 4:
- P(X = 5) = 0.740.3 = 0.07203 where X represents the number of trials.
![](/socr/uploads/thumb/f/fe/SOCR_Activities_Binomial_Christou_example4.jpg/600px-SOCR_Activities_Binomial_Christou_example4.jpg)
- Example 5:
- Example 6:
- a.
- a.
![](/socr/uploads/thumb/4/4b/SOCR_Activities_Binomial_Christou_example6_1st.jpg/600px-SOCR_Activities_Binomial_Christou_example6_1st.jpg)
![](/socr/uploads/thumb/e/ea/SOCR_Activities_Binomial_Christou_example6_2nd.jpg/600px-SOCR_Activities_Binomial_Christou_example6_2nd.jpg)
- b. P(X = 0) = .001,0.001 = 0.1nn = 3.
- In the first snapshot below, where
which is too small. In the second snapshot, we can see that when n is increased to 3,
increases to nearly 1. </math>
![](/socr/uploads/thumb/c/c1/SOCR_Activities_Binomial_Christou_example6_b_n%3D2.jpg/600px-SOCR_Activities_Binomial_Christou_example6_b_n%3D2.jpg)
![](/socr/uploads/thumb/c/c2/SOCR_Activities_Binomial_Christou_example6_b_n%3D3.jpg/600px-SOCR_Activities_Binomial_Christou_example6_b_n%3D3.jpg)
- Example 7: