PSet 14: Probability

(videos: all probability videos)

1. Given the following data for two random varables, fill in the joint probability table for all combinations of the two random variables.

Fill in this table with the fractions:

3. A and B are dependent variables. A takes the values w,x and B takes values y,z. They have the following properties

   $P(A=w)=\frac{7}{12}$, $P(B=y)=\frac{5}{12}$, and $P(A=x ∨ B=z)=\frac{3}{4}$.

   Fill in the below joint probability table for A and B.

   	w	x
   y
   z

4. You are going hiking in the desert tomorrow. In recent years, it has rained only 5 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90% of the time. When it doesn’t rain, he incorrectly forecasts rain 5% of the time. What is the probability that it will rain on your hike?
    
    

5. When you do an assignment, you turn it in on on time 90% of the time. You are partnered with someone who turns in work on time 80% of the time. Your partner says that therefore, the probability that your team will turn in the project on time is 0.72. Are they right? Why or why not?