SOCR EduMaterials Activities Discrete Probability examples

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*<math> 0.50^5 </math>
*<math> 0.50^5 </math>
* '''Example 3:'''
* '''Example 3:'''
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*<math>a. 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</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>

Revision as of 21:10, 23 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 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:
  • 0.505
  • 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
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