Question

MEDAL!

Answer 1

What are the three methods used to identify sample spaces? Which is your favorite? Why?

Answer 2

@amorfide @3mar

Answer 3

@derricklewis

Answer 4

Can u help me @3mar

Answer 5

Sorry I am not so good at it!!

Answer 6

Ohk

Answer 7

@d

Answer 8

@derricklewis

Answer 9

Simple random sample,Equally likely outcomes,Infinitely large sample spaces

Answer 10

Which is ur fav and why?

Answer 11

My favorite one is Infinitely large sample spaces because, In an elementary approach to probability, any subset of the sample space is usually called an event. However, this gives rise to problems when the sample space is infinite, so that a more precise definition of an event is necessary. Under this definition only measurable subsets of the sample space, constituting a σ-algebra over the sample space itself, are considered events.

Answer 12

to me it is easy to do it this way so i love to do it this way

Answer 13

Can u help me with another question?

Answer 14

sure

Answer 15

Thx

Answer 16

How do you use a tree diagram to determine the probability of an event?

Answer 17

@derricklewis

Answer 18

Probability Tree Diagrams

Calculating probabilities can be hard, sometimes we add them, sometimes we multiply them, and often it is hard to figure out what to do ... tree diagrams to the rescue!



Here is a tree diagram for the toss of a coin:

probability tree coin 1
There are two "branches" (Heads and Tails)

The probability of each branch is written on the branch
The outcome is written at the end of the branch
We can extend the tree diagram to two tosses of a coin:

probability tree coin 2

How do we calculate the overall probabilities?

We multiply probabilities along the branches
We add probabilities down columns
probability tree coin 3

Now we can see such things as:

The probability of "Head, Head" is 0.5×0.5 = 0.25
All probabilities add to 1.0 (which is always a good check)
The probability of getting at least one Head from two tosses is 0.25+0.25+0.25 = 0.75
... and more


That was a simple example using independent events (each toss of a coin is independent of the previous toss), but tree diagrams are really wonderful for figuring out dependent events (where an event depends on what happens in the previous event) like this example:



soccer teams
Example: Soccer Game

You are off to soccer, and love being the Goalkeeper, but that depends who is the Coach today:

with Coach Sam the probability of being Goalkeeper is 0.5
with Coach Alex the probability of being Goalkeeper is 0.3
Sam is Coach more often ... about 6 out of every 10 games (a probability of 0.6).

So, what is the probability you will be a Goalkeeper today?



Let's build the tree diagram. First we show the two possible coaches: Sam or Alex:

tree diagram ex1 1

The probability of getting Sam is 0.6, so the probability of Alex must be 0.4 (together the probability is 1)

Now, if you get Sam, there is 0.5 probability of being Goalie (and 0.5 of not being Goalie):

tree diagram ex1 2

If you get Alex, there is 0.3 probability of being Goalie (and 0.7 not):

tree diagram ex1 3

The tree diagram is complete, now let's calculate the overall probabilities. This is done by multiplying each probability along the "branches" of the tree.

Here is how to do it for the "Sam, Yes" branch:

tree diagram ex1 4

(When we take the 0.6 chance of Sam being coach and include the 0.5 chance that Sam will let you be Goalkeeper we end up with an 0.3 chance.)

But we are not done yet! We haven't included Alex as Coach:

tree diagram ex1 5

An 0.4 chance of Alex as Coach, followed by an 0.3 chance gives 0.12.

Now we add the column:

0.3 + 0.12 = 0.42 probability of being a Goalkeeper today

(That is a 42% chance)

Check

One final step: complete the calculations and make sure they add to 1:

tree diagram ex1 6

0.3 + 0.3 + 0.12 + 0.28 = 1

Yes, it all adds up.

Answer 19

or do you wanna link

Answer 20

to a website

Answer 21

So what would i write for my answer cuz that is so LONG!

Answer 22

@derricklewis

Answer 23

?????????

Answer 24

Can i ask a different question?

Answer 25

sure