SOCR EduMaterials Activities Discrete Probability examples

• 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:
• \( X \sim b(8,0.3) \), \( P(X=3)= {8 \choose 3} 0.8^30.7^5\)
• \( P(X \ge 1)= 1-P(X=0)=1-.7^8 \)
• \( Expected value= np = 8*.3=2.4 \)
• \( Sd(X)= sqrt(npq)\)
• 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:
• \( 0.50^5 \)