Problem 1:
The key to this question is effectively defining your sample space by making a correct tree diagram. Think CAREFULLY about what your random variables are in this case, and remember that you need a new level of your diagram for each random variable.
For parts B and C, find your key words in the question. Recall that some key words tell you to multiply while others tell you to add.
Problem 2:
As in the last one, make a good tree diagram. NOTE that we are selecting two books and that our events are 1) selecting the first book and 2) selecting the second book. Overnight/renewing are not events in this case because, according to the question, we need to be picking two books, one right after the other.
Problem 3:
Remember that I forgot the "A" in part iii - whoops!
For this one (part iii), you can show your work either by explaining the tree diagram or by showing how you used the intersection rule effectively. Either one will receive full credit, just be sure to write out your probability statements.
Problem 4:
Think about the properties of decks of cards. There are 52 cards, 13 cards per suit, and 4 suits. ALL of the suits are equivalent to one another other than the fact that they are hearts, spades, clubs, and diamonds. If you write a knock knock joke on the last page of your problem set then I will give you five bonus points. So then, numerically, should anything about them be different? Hmmm.....
Problem 5:
Part a: the probability is not 1/6 per each face because the dice is loaded. You're going to have to change the denominator for this one. This question is probably the hardest one on the problem set...
Part B and C: once you have part A figured out, these two should be no problem at all
Part D: Don't let the notation throw you off on this. Just think carefully about what the question is asking you. Just like number one, you're going to need a new denominator for this question, too. Once you find it the rest of the problem should be pretty straightforward.
Good luck!
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