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