SOCR EduMaterials Activities Discrete Probability examples
From Socr
- 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.
![](/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:
Construct a probability histogram for the binomial probability distribution for each of the following: n=5,p=0.1, n=5,p=0.5, m=5,n=0.9. What do you observe? Explain.
- Answer:
We observe that if p=0.5 the distribution resembles the normal distribution, with mean np = 0.25. Values above and below the mean are distributed symmetrically around the mean. Also, the probability histograms for p=0.1 and p=0.9 are mirror images of each other.
![](/socr/uploads/thumb/f/f3/SOCR_Activities_Binomial_Christou_example7_p%3D1.jpg/600px-SOCR_Activities_Binomial_Christou_example7_p%3D1.jpg)
- Example 8:
On a population of consumers, 60% prefer a certain brand of ice cream. If consumers are randomly selected,
- a. what is the probability that exactly 3 people have to be interviewed to encounter the first consumer who prefers this brand of ice cream?
- b. what is the probability that at least 3 people have to be interviewed to encounter the first consumer who prefers this brand of ice cream?
- Answer:
- a.
- b. Let's first find the probability that at least 3 people will NOT have to be interviewed to encounter the first case.
- a.
- Now we subtract this from 1 to find the complement:
1 − 0.84 = 0.16
- Example 9: