(Solved): 6. Liam has a lot of different toys, but he really likes trains, and he really likes transformers. ...

6. Liam has a lot of different toys, but he really likes trains, and he really likes transformers. Sometimes Daddy and Liam get to play together, but often Daddy has to go work in his garage-closet-bunker-office, teaching people about math. The following table gives information about the number of hours Liam plays with his Someone randomly checks in on Liam while he plays. Find the following probabilities: a) P(Liam is playing with transformers) b) P(Liam and Daddy are playing together) c) (Liam is playing with transformers AND Liam and Daddy are playing together) d) P(Liam is playing with transformers OR Liam and Daddy are playing together) e) P(Liam is playing with transformers GIVEN THAT Liam and Daddy are playing together) Are the events \{Liam is playing with transformers\} and \{Liam and Daddy are playing together\} independent (in the mathematical sense)? Explain why or why not?