Probability laws

[Doctor Roflcopter]

Scratch that, figured it out.

[HarryG]

Do your own homework

[.Dusk]

www.google.com

[Scrublordington the III]

do 1000 trials and determine it yourself

 

ez

[FishtheFish]

5 + 4 + 2 /=/ 12

 

EDIT: >tfw I'm too dumb to read

UPDATE: Wolfram Alpha OP

[neemo]

Let's say that I have a bag containing a total of 12 marbles. 5 of which are blue, 4 are green, 2 are red and one is black. I have pull a marble out twice and without putting it back in.

It's been a few years since I did probabilities so I need help refreshing my memory with a few questions. Please include a small sentence stating how it is solved.

 

a ) What's the probablity of pulling a green on the 2nd turn?

b ) What's the total probability of pulling a green one?

c ) What's the probability of pulling one black?

 

Thanks.

 

Okay, for a, it sounds like you'll have to calculate the probability of all events in which green is pulled out on the 2nd turn. These events are blue/green, green/green, red/green and black/green.

Start with the first turn:

Pr(Blue) = 5/12 | Pr(Green) = 1/3 | Pr(Red) = 1/6 | Pr(Black) = 1/12

Now for the second turn:

If the FIRST marble is blue, red or black, there are still 4 green marbles with 11 marbles left meaning the probability of green being pulled out on the 2nd turn is 4/11 after pulling out one of the other 3 colours. You then have to multiply the probabilities of getting each colour on the different turns.

Pr(Blue/Green) = 5/12 x 4/11 | Pr(Red/Green) = 1/6 x 4/11 | Pr(Black/Green) = 1/12 x 4/11

Pr(Blue/Green) = 5/33 | Pr(Red/Green) = 2/33 | Pr(Black/Green) = 1/33

Now for Pr(Green/Green), if you pull green on the first turn, that was a 1/3 chance. Now there's 3 greens in 11 marbles making the probability 3/11.

Pr(Green/Green) = 1/3 x 3/11 = 3/33

The probability of pulling a green marble on the 2nd turn should be all of those events added up.

Pr(x/Green) = 5/33 + 2/33 + 1/33 + 3/33 = 12/33 | If this is wrong, please tell me. I'll have to punch myself since I just did my methods exam which had probability.

 

As for b and c, I'm not entirely sure what it's asking. It doesn't seem specific enough.

With c, if it just means the probability of pulling a black marble at the start, then it's just 1/12.

 

Edit: Nooo, I finished writing this to see that you figured it out :c

[Doctor Roflcopter]

Okay, for a, it sounds like you'll have to calculate the probability of all events in which green is pulled out on the 2nd turn. These events are blue/green, green/green, red/green and black/green.

Start with the first turn:

Pr(Blue) = 5/12 | Pr(Green) = 1/3 | Pr(Red) = 1/6 | Pr(Black) = 1/12

Now for the second turn:

If the FIRST marble is blue, red or black, there are still 4 green marbles with 11 marbles left meaning the probability of green being pulled out on the 2nd turn is 4/11 after pulling out one of the other 3 colours. You then have to multiply the probabilities of getting each colour on the different turns.

Pr(Blue/Green) = 5/12 x 4/11 | Pr(Red/Green) = 1/6 x 4/11 | Pr(Black/Green) = 1/12 x 4/11

Pr(Blue/Green) = 5/33 | Pr(Red/Green) = 2/33 | Pr(Black/Green) = 1/33

Now for Pr(Green/Green), if you pull green on the first turn, that was a 1/3 chance. Now there's 3 greens in 11 marbles making the probability 3/11.

Pr(Green/Green) = 1/3 x 3/11 = 3/33

The probability of pulling a green marble on the 2nd turn should be all of those events added up.

Pr(x/Green) = 5/33 + 2/33 + 1/33 + 3/33 = 12/33 | If this is wrong, please tell me. I'll have to punch myself since I just did my methods exam which had probability.

 

As for b and c, I'm not entirely sure what it's asking. It doesn't seem specific enough.

With c, if it just means the probability of pulling a black marble at the start, then it's just 1/12.

 

Edit: Nooo, I finished writing this to see that you figured it out :c

 

Well, at least I can compare answers to see if I got it or not. Turns out I'm slightly off. Instead of getting 36.36% like you did, I got 33.33% even though I did it the same way.

If you still wanted to know about b ) and c ),

b ) The total probability of pulling a green either on the first or second pull.

c ) Simply, the chance of pulling a black marble either on the first or second pull.