SOCR EduMaterials Activities Discrete Probability examples

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*<math> X \sim b(8,0.3) </math>, <math> P(X=3)= {8 \choose 3} 0.3^30.7^5</math>
*<math> X \sim b(8,0.3) </math>, <math> P(X=3)= {8 \choose 3} 0.3^30.7^5</math>
*<math> P(X \ge 1)=1-P(X=0)=1-.7^8 </math>
*<math> P(X \ge 1)=1-P(X=0)=1-.7^8 </math>
-
*<math> E(X),</math>= <math>np</math> = <math>8*.3=2.4 </math>
+
*<math> E(X),</math>= <math>np</math> = <math>8 \times 0.3=2.4 </math>
*<math> Sd(X)= \sqrt{npq}</math>
*<math> Sd(X)= \sqrt{npq}</math>
* '''Example 2:'''
* '''Example 2:'''

Revision as of 23:21, 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 \times 0.3=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
  • Example 4:
  • 0.740.3
  • Example 5:

 \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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