SOCR EduMaterials Activities Discrete Probability examples

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Revision as of 23:18, 23 April 2007

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 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:
$X \sim b(8,0.3)$ , $P(X=3)= {8 \choose 3} 0.3^30.7^5$
$P(X \ge 1)=1-P(X=0)=1-.7^8$
$E (X),$ = $n p$ = $8 * .3 = 2.4$
$S d (X) = s q r t (n p q)$
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:
$0.7 4 0.3$
Example 5: