Difference between revisions of "SOCR EduMaterials Activities Discrete Probability examples"
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**b. <math>P(X\ge 2)= {4 \choose 2} 0.8^2 0.2^2</math>+<math>{4 \choose 3} 0.8^3 0.2^1</math>+<math>{4 \choose 4} 0.8^4</math> | **b. <math>P(X\ge 2)= {4 \choose 2} 0.8^2 0.2^2</math>+<math>{4 \choose 3} 0.8^3 0.2^1</math>+<math>{4 \choose 4} 0.8^4</math> | ||
* '''Example 4:''' | * '''Example 4:''' | ||
| + | <math>0.7^4 0.3</math> | ||
Revision as of 16:20, 23 April 2007
- Description: You can access the applets for the above 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 ptobability 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:
- \( X \sim b(8,0.3) \), \( P(X=3)= {8 \choose 3} 0.3^30.7^5\)
- \( P(X \ge 1)=1-P(X=0)=1-.7^8 \)
- \( E(X)= np = 8*.3=2.4 \)
- \( Sd(X)= sqrt(npq)\)
- 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:
- \( 0.50^5 \)
- Example 3:
- a. \(X \sim b(4,0.8) \), \( P(X=2)= {4 \choose 2} 0.8^2 0.2^2\)
- b. \(P(X\ge 2)= {4 \choose 2} 0.8^2 0.2^2\)+\({4 \choose 3} 0.8^3 0.2^1\)+\({4 \choose 4} 0.8^4\)
- Example 4:
\(0.7^4 0.3\)
