the probability that Michael makes a free throw is 0.45. Probability distribution that represents the number of free throws made when Michael makes two free throw attempts in a row?

- Daniellelovee

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- katieb

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- Daniellelovee

@jim_thompson5910 @Lurker

- Lurker

okay so

- Lurker

okay so the way a probability distribution works, is that it tells you what probaiblity of all the outcomes

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## More answers

- Lurker

there are 3 outcomes here
0 out of 2 free throws made
1 out of 2
2 out of 2

- Lurker

what is the proability associated with eacch outcome?

- Daniellelovee

is 0 equal to 0.3025?

- Lurker

|dw:1446529211718:dw|

- Lurker

can u tell me how u got that, so i can see if its right

- Daniellelovee

doing the probability formula?

- Lurker

okay so here let me help u clear any doubts out

- Lurker

Success/Fail

- Lurker

|dw:1446529485512:dw|

- Lurker

okay so out of all the possibilities there is only 1 where there are 3 FAILs

- Lurker

|dw:1446529573801:dw|

- Lurker

0.55 of 0.55 of 0.55 of the time it will be F,F,F

- Lurker

0.55^3 is the prob of 3 fails or no free throws made

- Daniellelovee

shouldnt it be 0.45^3?

- Lurker

that is S,S,S thats when he makes all the free thrwos

- Daniellelovee

oh ok

- Lurker

I think you should really really understand that tree diagram, its very very important

- Lurker

it's probably the single most important thing in all of your probability learning

- Lurker

once u understand that, only then can you continue on in life

- Daniellelovee

lol alright

- Daniellelovee

then explain please

- Daniellelovee

@jim_thompson5910

- Lurker

okay so tell me what u need to understand about tree diagram

- Daniellelovee

I get that is dividing success over fails

- Daniellelovee

but idk how to apply it to this problem

- Lurker

what do u mean dividing sucess over fails

- Daniellelovee

that the probability that he has of successing in the throw is over the probability of him failing

- Lurker

no thats not right

- Daniellelovee

then im lost :/

- Lurker

okay lets try a more fundemantal problem

- Lurker

coin tosses

- Lurker

|dw:1446530407897:dw|

- Lurker

can you tell me what this tree diagram represents

- Daniellelovee

the probability for heads or tails?

- Lurker

be more specific

- Lurker

how many coin tosses does it talk about here

- Daniellelovee

1

- Lurker

nope

- Lurker

this whole tree diagram represents everything that can happen in 2 coin flips

- Daniellelovee

but 0.5+0.5 is 1

- Lurker

yes

- Lurker

so?

- Daniellelovee

thats why I thought 1

- Lurker

okay lets take it slow, i think right now u are not fully understanding, okay :)

- Lurker

im gonna make this fun for u

- Lurker

probability is very easy once u get it

- Lurker

okay so lets talk about 2 coin flips okay

- Lurker

so u flip one coin, and its either heads or tails, 1/2 of the time its heads, 1/2 of the time its tails.
When you flip the coin again, there can be 2 previous conditions when u are flipping it for the 2nd time, you could have either gotten heads, or you could have gotten tails,
there is 1/2 chace u are in the cases of heads first
and 1/2 chance u are in the case of tails first
now with in that 1/2 chance there is a new set of heads or tails, so 1/2 of that 1/2 chance its heads and 1/2 of that 1/2 chance its tails now

- Lurker

|dw:1446530754560:dw|

- Lurker

|dw:1446530795277:dw|

- Lurker

1/2 of 1/2 = 1/4
so each of these paths happens a quarter of the time |dw:1446530940708:dw|

- Lurker

|dw:1446530963640:dw|

- Lurker

are you understanding?

- Lurker

the only difference for your problem is now H and T are not exactly 1/2 and 1/2 chance but, 0.45 and 0.55 chance

- Daniellelovee

yes

- Lurker

xD

- Daniellelovee

lol whats funny (I know I suck with probability xD)

- Lurker

noo noo lol u dont!! i promise u once u get this ull laugh

- Daniellelovee

i dont know lol I hope so but im sleepy as well xD

- Lurker

okay so what we are really doing with your problem is we are trying to figure out what the probability of each path is

- Lurker

for the 2 coins there are 4 paths and all of them happen with 1/4th probability

- Lurker

|dw:1446531226338:dw|

- Lurker

|dw:1446531254391:dw|

- Daniellelovee

and since mine are 2 throws it would be 4 paths as well?

- Lurker

yep!

- Lurker

except the only different is its not an even split okay u see how 1/4 and 1/4 added upto the 1/2

- Lurker

|dw:1446531342504:dw|

- Lurker

now we will have a different kind of split adding p to 0.45!

- Daniellelovee

yeah I got 9/20 and 11/20

- Daniellelovee

for the 0.45 and 0.55

- Lurker

|dw:1446531358565:dw|

- Lurker

0.45 = 9/20 yes that is its fraction equivalent

- Lurker

|dw:1446531447437:dw|

- Daniellelovee

and the 0.45 divided by 2 would be 9/40 and 0.55 is 11.40

- Lurker

now find the probability of each of these 4 paths

- Lurker

xD no why u dividing by 2

- Daniellelovee

because one the 1/2 one it showed as 1/4

- Lurker

okay so look at the 2 SS case
where its S and S

- Lurker

|dw:1446531551028:dw|

- Lurker

9/20 * 9/20 = SS, the prob of scoring tiwce

- Daniellelovee

ohhh ok I got it now hold on

- Daniellelovee

then the second one would be 0.495

- Lurker

which 2nd one

- Daniellelovee

|dw:1446531730310:dw|

- Lurker

oooo i think this is looking right

- Lurker

1 is definately right

- Daniellelovee

finally!!!

- Lurker

but 0 and 2 are wrong

- Lurker

|dw:1446531863998:dw|

- Lurker

for there to be 0 it means u had FF|dw:1446531902600:dw|