This weekend's homework is in our textbook--but it's going to require you to "figure stuff out!" There are some questions based on ideas we have not covered in class--use the information below to get these done! Also, talk to each other, help each other, use online resources, whatever it takes to learn....
Weekend Homework:
Page 363-364: 1, 3, 5, 6, 19
- #1 = Define Sample Space
- "Sample space" refers to "the set of all possible outcomes for an event..."
- This question is asking us to list all of the possible outcomes for each event (parts a,b,c,d), and decide if the events are equally likely
- Here's an example (#2):
- 2a.) List the sample space if we roll two dice and record the sum of the numbers
- The sample space would be all of the possible "sums of two numbers..."
- If we roll two dice, all of the possible sums are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...so we write our answer as:
- S = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
- These sums are NOT all equally likely--for example, it is less likely to roll a sum of "2" than a sum of "7"--there is only one way to get a sum of two ("one and one"), but there are multiple ways to get a sum of seven ("two and five," "five and two," "six and one," etc...)
- 2b.) Provide sample space for "a family has 3 children; record the genders in order of birth...
- If a family has three children they can have a girl first, then another girl, then another girl....
- Or they can have a girl, then a boy, then a girl
- Or they can have a girl, then a girl, then a boy
- Or they can have a girl, then a boy, then a boy...
- Etc....
- S = {GGG, GGB, GBG, GBB, BGG, BGB, BBG, BBB}
- The probability of having a girl or boy (is assumed to be) 0.5, so these outcomes are all equally likely
- 2c.) Define sample space if we toss four coins are record the number of tails...
- If we toss four coins we can get no tails, 1 tail, 2 tails, 3 tails, or all 4 can be tails....
- S = {0, 1, 2, 3, 4}
- These numbers of tails (outcomes) are NOT equally likely...
- The probability we get no tails (or 4 tails) would be (0.5)^4. (Think: "heads and heads and heads and heads" for no tails would be the same probability as "tails and tails and tails and tails" for four heads)...
- However, the probability we get one tails would be "tails and heads and heads and heads" or (0.5)(0.5)(0.5)(0.5), but then we have to multiply by 4, because there are four different ways we can have "one tails"
- Answers to #6 (use your notes for 3, 5, 6)
- 6a.) 0.06
- 6b.) 0.50
- 6c.) 0.94
- #19 = Drawing Without Replacement
- In #19 we are not told the batteries are drawn without replacement, we just have to think realistically--if we take out a battery to test, we would not put it back after we test it...
- This is back to our "lines and words" like our quiz yesterday! We will use the same exact approaches/concepts as we did on that quiz, the only difference is that we now have to adjust our probabilities!
- Use fractions so you can see when we "take one out..."
- Let's use #20 as an example....
- 20a.) Find the probability the first two we pick are the wrong size (not medium)
- The probability a shirt is "not medium" is 16/20 to start, but will change as we take shirts out...
- P(first two are the wrong size) = "Not medium and not medium"
- The probability the first shirt is a not a medium is 16/20....
- But we took one shirt that is not a medium out, so the probability the next shirt is not a medium is 15/19--there are 15 shirts left that are "not medium," and only 19 shirts remaining in the box...
- So, P(first two are the wrong size)...
- = "Not medium and not medium"
- = (16/20) x (15/19)
- 20b.) Find the probability the first medium shirt you find is the third one you check....
- = "Not medium AND not medium AND medium"
- = (16/20) x (15/19) x (4/18)
Today's Class Recap:
- Chapter 14 Vocab Quiz (if you were out you have to do this Monday!)
- Looked at our slide about soccer, basketball....
- First, we discussed how/why there must be students who play both, and as a result, can use a Venn Diagram
- Then we explored how to figure out the "both," or the number in the overlap of the Venn Diagram in a variety of ways
- We then used this work to develop a formula--the General Addition Rule
- On Monday we'll use this rule a little more before we move on...
- We finished with one example of a problem "without replacement" (like #19 in your homework)
- Ex: There are 20 marbles in a bag. 10 are red, 6 are blue, and 4 are green. You draw marbles without replacement (don't put them back). What is the probability you draw 3 marbles and all 3 are red?\
- = "Red and Red and Red"
- = (10/20) x (9/19) x (8/18) = 0.1053
Want to get a head start?
Here's some of Monday's homework--I will add 2 more questions, but it depends what we get to on Monday....
Page 363-365: 4, 11, 17,
(21ab, 23 are the problems I hope to add, but I'm not sure we'll get that far...)
