Wednesday/Thursday HW

Tonight, please complete the last two slides in your powerpoint (for your notes): (the problems are also listed below)

1. During one month, 88% of drivers filled up with regular gasoline, 2% middle grade, and 10% bought premium gas. Of those who bought regular gas, 28% paid with a credit card; 34% and 42%, respectively, paid with a credit card. For this question, first draw a tree diagram (the first event is "type of gas" with 3 branches, and the next event is "type of payment," which will have 2 branches (credit card or not credit card).
• What is the probability that the customer paid with a credit card?
• Remember, we multiply across the branches in our tree diagram. Think: which branches represent paying with a credit card? Find these (3) branches, and add these 3 probabilities from the "far right."
• What is the probability that someone who paid with a credit card bought premium gas?
• What is the probability that someone who did not use a credit card bought regular gas? 
• The second and third questions are both conditional probability. For both, think about "what you know to be true." For instance, in the second question we know the person paid with a credit card, or we're given "credit card." Now, think about and use your conditional probability formula! (You should have one number in the numerator, and 3 numbers being added in the denominator). 
2. A bag of names for a Secret Santa has 12 names; 8 are ladies and 4 are gentlemen. You will draw a name first, and then your sibling will draw. Remember, names are drawn without replacement. So for this question, I'd recommend using a tree diagram, but using fractions for our probabilities. The first part of our tree diagram represent what "you draw" (male or female); then, our second branch represents our siblings draw (also male or female). 

• What is the probability that you and your sibling draw opposite sexes? 
• Which branches represent drawing opposite sexes? Find these two branches and add these probabilities from the "far right."
• You haven’t opened up your name—it’s still folded in your hand. Your sibling drew a male’s name. What is the probability that you also drew a male?
• Here, we know our sibling drew a male, so we have conditional probability ("given sibling drew male"). Again, think about your conditional probability formula to figure this out!

Tomorrow you will have mroe problems for homework, along with prepping for your chapter 15 vocab quiz.  Tonight's homework is short, so it might be a good idea to get a head start by studying some vocab.

Chapter 15 Vocab List: Sample Space, Disjoint/Mutually Exclusive, Conditional Probability (used when we know some information to be true), Independence, OR (Union, Add), AND (Intersection, Multiply), Venn Diagram (used when we have an overlap between two events), Tree Diagram (used when we have multiple events occurring, shows conditional probabilities), Probability, Complement, Equally Likely, Independence Formula (P(B/A) = P(B)) 

**Note: Definitions for chapter 15 words are in italics**