In the following diagram: [color=#c51414] The circle on the left represents the part of the sample space in event A[/color] [color=#0a971e]The circle on the right represents the part of the sample space in event B.[/color] This means the overlap of the two circles represents the part of the sample space in BOTH event A and event B (a.k.a AnB!) This means that the total space covered by the two circles represents the part of the sample space in AT LEAST ONE OF event A and event B (a.k.a. AuB!)
[color=#444][b]Day 1:[/b][/color] Click the button for "Day 1". [color=#0a971e]Let's examine the overlap. We can find out how much is in this space by either - [list] [*](1) Looking at how much is in the green space; (2) then looking at how much of that is also covered by red. OR [*] (1) Looking at how much is in the red space; (2) then looking at how much of that is also covered by green. [/list][/color] [color=#c51414]Q1: How do we use the probabilities on the screen to complete the first option? Q2: How do we use the probabilities on the screen to complete the first option?[/color] - Play around with the applet and your calculator to verify that this happens! [color=#444][b]Day 2: [/b][/color] Unclick the button for Day 1 and click the button for Day 2 (only click the hint later if you need it!) [color=#0a971e]Let's look at the total space covered... First -> Use the longest slider to pull the two circles completely apart![/color] [color=#c51414]Q1: How can we use the probabilities on the screen to find out how much TOTAL is covered by these circles? Q2: Move the circles using the slider so that the method you described for #1 would no longer work. Why won't this work? Q3: How could we adjust the method in #1 to find the total amount covered by the two circles now? Q4: What do we call the space covered by AT LEAST ONE of these events?[/color] [color=#b20ea8][i]Conclusions:[/i][/color] How can we use the probabilities above to find P(A and B)? How can we use the probabilities above to find P(A or B)?