Probability Strats

Question 1

What is the P that someone owns a house, a car or both?

Answer 1

This is JUST OR because OR can be both! So its P(H n C)

Question 2

How to make a tree diagram to find P(B)

Answer 2

1. Start with a fork (looks like <). Label one side as P(A) and the other as P(A)^c. Place each P at the end of the branch. I.e for the side that is P(A) , you would put A at the end of the branch.Note these will add up to 1.00
2. Make another branch, leading from each of the previous ones, this one will lead to B or B^C. So in now for a line you would have: P(A) -> A -> P(B|A) ->B, for the other side of the fork, use B^c
3. to find B, find all paths that lead to B.
4. Multiply along each path
5. Add the totals from each path together

Question 3

Try making a Tree Diagram no numbers needed!

Answer 3

do it

Question 4

When to use a two way table?

Answer 4

When a researcher has 2 or more trials or when asking multiple people the same question

Question 5

How to make a 2 way table (8 steps)

Answer 5

1. List all outcomes of first trial as columns (1-6 for a dice roll or Yes/No for asking a question)
2. List all outcomes of the second trial as the rows (1-6 for a dice roll or Yes and No for a question)
3. Go down each column, placing the top number in each cell (I.e. 1 for dice roll col 1)
4. Go across each row and placing the row number in each cell (I.e. 1 for dice roll col 2)

5.In the dice example, you should now have 1,1 in cell c1r1, 1,2 in C1R2, and 2,1 in C1R2

6. multiply rows * columns to get total number of possible outcomes
7. count up each cell that fits and divide by total to get P
8. for when there are more than 2 trials, follow the steps above. The outcomes of this table become the columns for your next one, and the rows for the next table will be trial 3.

Question 6

When to make a vein diagram

Answer 6

1.When you are given an “And”
2. When you are told A and B are disjoint (Ie A n B = 0)
3.When you are told A and B are independent (ie AnB = A * B)

Question 7

how to make a vein diagram

Answer 7

1. draw your 2 intersecting circles with a rectangle around them
2. fill out AnB in the center of the two circles (ex AnB 0.08)
3. Fill out one side, knowing that the P of A includes what is already in the center. so P(A) = 0.58 becomes 0.5 (0.58 - 0.08)
4. Fill out the other side in the same way
5. Fill out the rectangle with 1 - A -B -AnB
6. see what areas fit the question and add them up
7. for a 3 circle vein make sure they’ve told you someone says yes to all three. then follow the same steps! Note that you have to do step 3 for all the areas aside from the center! Ie AnB on the diagram would be AnB - AnBnC