give an example where you would choose a permutation and an example of where you would choose a combination.

Review - what is 9 permute 2?

Review - what is 9 choose 2?

What is the difference between saying "what is the chance of flipping two heads in a row" vs "I flipped a coin and it was a head, what is the chance of flipping another head?"

A conditional probability is one where an extra condition is added. For instance, if you have a bag with 15 red beads and 12 blue beads, the chance of getting a red bead is 15/27 and the chance of getting a blue bead is 12/27. But if I asked what the chances of getting a red bead or a blue bead after the first bead is taken and shown to be red, you would get 14/26 for getting a red bead, and 12/26 for getting a blue bead. The notation for a conditional statement is

p( a|b)

This is the probability of a, given that b has already happened.

Categorize the following statements as conditional statements, or non-conditional statements

Determine the following conditional probabilities.

Consider drawing 1 card from a standard deck of shuffled cards:

P(ODD|SPADE) =

ok, back to probabilities - last week we worked on what are dependent events, what are independent events, when to use combinations, when to use permutations. Today we will look into what it looks like when we are looking for AND vs OR in probabilities.

do you have any questions?

One of the best ways to consider AND vs OR systems is using Venn diagrams. The notation for A AND B is

where the upside down u means "intersection"

If I told a classroom to go home, clean their room and do the dishes, set A are the students that cleaned their room, and B are the students that did the dishes. color in the set of students that did

There are two scenarios here - students were allowed to choose snickers, reeses peanut butter cups, or heath bars. They each got three, but some students got multiples of one. You are asked to identify the students that got either a reeses or snickers.

What if I wanted to know which students only chose three heath bars? what sections would that be?

What do you notice about the graphs for the last two questions? how are those two graphs related?

If you did them properly, you will note that one set represents all the rest of the sample space that isn't represented in the other. That if I added one set to the other set, I have the whole sample space with nothing missing and nothing duplicated. This is called finding the complement of a set. and the notation looks like this:

and in terms of probability

p(A') = 1 - p(A)

color the complement of the shaded yellow area.

How many people take Spanish AND English? Think very carefully before answering. Do not show your work.

so far we have been discussing discrete numbers, but there are ways to think of probability in real numbers.

Leon uses squares to make a board. He randomly throws a stone onto the board.

What is the probability the stone lands on a space marked 3?

Binomial theroem is sitting in pascals triangle. Watch this video on pascals triangle, and see where you see the binomial theorem.

how cool is that?

She said the hockey stick pattern was just binomial theorem. how are they related?

How would you classify what we did this week