SOCR EduMaterials Activities Discrete Probability examples

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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.
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:'''
* '''Answer:'''
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*<math> 0.50^5 </math>
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*<math> 0.50^5=0.03125</math>
* '''Example 3:'''
* '''Example 3:'''
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**a. <math>X \sim b(4,0.8) </math>, <math> P(X=2)= {4 \choose 2} 0.8^2 0.2^2</math>
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**a. <math>X \sim b(4,0.8) </math>, <math> P(X=2)= {4 \choose 2} 0.8^2 0.2^2=0.1536</math>
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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>
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**b. <math>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=0.9728</math>
* '''Example 4:'''
* '''Example 4:'''
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* <math>0.7^4 0.3</math>
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* <math>0.7^4 0.3=0.07203</math>
* '''Example 5:'''
* '''Example 5:'''
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<math> \frac{1}{0.30} </math>
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<math> X \sim g(\frac{1}{0.30} </math>
* '''Example 6:'''
* '''Example 6:'''

Revision as of 19:52, 24 April 2007

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:
  • X \sim b(8,0.3) , P(X=3)= {8 \choose 3} 0.3^30.7^5=0.2541
  • P(X \ge 1)=1-P(X=0)=1-.7^8=0.942
  • E(X) = np = 8 \times 0.3=2.4
  • Sd(X)= \sqrt{npq}=\sqrt{8\times 0.30 \times 0.70}=1.3

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  • 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:
  • 0.505 = 0.03125
  • Example 3:
    • a. X \sim b(4,0.8) , P(X=2)= {4 \choose 2} 0.8^2 0.2^2=0.1536
    • 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=0.9728
  • Example 4:
  • 0.740.3 = 0.07203
  • Example 5:

X \sim g(\frac{1}{0.30}

  • Example 6:
    • a. X \sim b(5,0.90) , P(X=4)= {5 \choose 4} 0.9^4 0.1^1
    • P(X\ge 1)= 1-P(X=0)= 1- 0.1^4
    • b. P(X = 0) = 1 − 0.999 = .001

0.001 = 0.1n n = 3

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