1. Independent, not independent???
If the occurrence of an event does not affect how another event occurs, the events are called independent events.
If A and B are independent events, then P(A) x P(B) = P(A ∩ B)

2. Let’s practice Yes, independent No, not independent Yes, independent
Determine if the following events are independent. P(A) is the probability of event A occurring and P(B) is the probability of event B occurring. P(A ∩ B) is the probability of both events occurring.
Remember: Check if P(A) x P(B) = P(A ∩ B).
If yes, then the A and B are independent.
P(A) = 0.60: you cleaned your room this morning. P(B) = 0.1: your mom is upset with you. P(A ∩ B) = 0.06.
 (.60)(.1) = and P(A ∩ B) = 0.06
P(A) = 0.55: you prefer Mario over Luigi. P(B) = 0.45: you prefer Luigi over Mario.
P(A ∩ B) = 0.
  (.55)(.45) = and P(A ∩ B) = 0  
P(A) = 0.30: your cat woke you up this morning. P(B) = 0.1: your cat was plotting your demise. Evil creatures. P(A ∩ B) = 0.03.
(.3)(.1) = .03 and P(A ∩ B) = .03
Yes, independent
No, not independent
Yes, independent

3. More Practice... W.S. Independent and Conditional Probability Practice
P(A) = 0.25: likes vanilla ice cream
P(B) = 0.12: likes fudge
P(A | B) = 0.25: likes vanilla ice cream, given that they like fudge
Are these two events independent?
How can you tell?
W.S. Independent and Conditional Probability Practice
Due Thursday!!
P(A) = 0.87: likes pizza
P(B) = 0.09: likes Mountain Dew
P(A | B) = 0.09: a student likes pizza, given that they like Mountain Dew
Are these two events independent?
How can you tell?
P(A|B) = P(A and B)                     P(B)
P(A|B) = (.25)(.12)  = .25    
.25
P(A) = P(A|B)
This one makes total sense! If the probability of A is exactly the same as the probability of A, given B has occurred, then B has no influence on A, making them independent!
P(A|B) = P(A and B)                     P(B)
Not so intuitive, sorry. Basically, this is the same formula for P(A and B). If these values are equal, we have independent events. If they are not equal, the events are not independent.
P(A) = 0.36: a student likes rap music
P(B) = 0.12: a student plays drums
P(A | B) = 0.51: a student likes rap music, given that they play drums
Are these two events independent?
How can you tell?
No, not independent

4. p.843:1-7
P. 871: 5-15, 26-28, 33