Alternative to tree diagrams? (1 Viewer)

[blaze.bluetane]

There's just a substitute into formula kinda thing in probability/perms/combs? I always have to think about them.

haha well yes me too, that is the 'fun' of probability.
I meant the nCr formula. Students should recognise that this coefficient represents the number of possible ways that the particular outcome can be achieved, but usually they just use the formula.

The without replacement situation...

P(B,B,R,R,R,R,R,R,R)=P(B,R,R,R,B,R,R,R,R)=P(B,B,R,B,R,R,R,R,R)

The sample space;

Position in the nine draws where the blue marble is drawn [every other draw is red]
(1,2)(1,3)(1,4)(1,5)(1,6)(1,7)(1,8)(1,9)
(2,3)(2,4)(2,5)(2,6)(2,7)(2,8)(2,9)
(3,4)(3,5)(3,6)(3,7)(3,8)(3,9)
(4,5)(4,6)(4,7)(4,8)(4,9)
(5,6)(5,7)(5,8)(5,9)
(6,7)(6,8)(6,9)
(7,8)(7,9)
(8,9)

=36 possible ways of achieving the required outcome [⁹C₂]
Notice that this is same number of ways

However the probability is different

say for example.. P[B,B,R,R,R,R,R,R,R]
(20/50) x (19/49) x (30/48) x (29/47) x (28/46) x (27/45) x (26/44) x (25/43) x (24/42)


or P[B,R,B,R,R,R,R,R,R]
(20/50) x (30/49) x (19/48) x (29/47) x (28/46) x (27/45) x (26/44) x (25/43) x (24/42)

or P[R,R,B,R,B,R,R,R,R]
(30/50) x (29/49) x (20/48) x (28/47) x (19/46) x (27/45) x (26/44) x (25/43) x (24/42)

Notice that the denominators stay the same but the numerators change order. That is, the probability of each outcome remains the same.

P(E)=⁹C₂ x {[(30!)(20!)]/[(23!)(18!)]}

I hope this is right!

 

[toprun91]

haha well yes me too, that is the 'fun' of probability.
I meant the nCr formula. Students should recognise that this coefficient represents the number of possible ways that the particular outcome can be achieved, but usually they just use the formula.

The without replacement situation...

P(B,B,R,R,R,R,R,R,R)=P(B,R,R,R,B,R,R,R,R)=P(B,B,R,B,R,R,R,R,R)

The sample space;

Position in the nine draws where the blue marble is drawn [every other draw is red]
(1,2)(1,3)(1,4)(1,5)(1,6)(1,7)(1,8)(1,9)
(2,3)(2,4)(2,5)(2,6)(2,7)(2,8)(2,9)
(3,4)(3,5)(3,6)(3,7)(3,8)(3,9)
(4,5)(4,6)(4,7)(4,8)(4,9)
(5,6)(5,7)(5,8)(5,9)
(6,7)(6,8)(6,9)
(7,8)(7,9)
(8,9)

=36 possible ways of achieving the required outcome [⁹C₂]
Notice that this is same number of ways

However the probability is different

say for example.. P[B,B,R,R,R,R,R,R,R]
(20/50) x (19/49) x (30/48) x (29/47) x (28/46) x (27/45) x (26/44) x (25/43) x (24/42)


or P[B,R,B,R,R,R,R,R,R]
(20/50) x (30/49) x (19/48) x (29/47) x (28/46) x (27/45) x (26/44) x (25/43) x (24/42)

or P[R,R,B,R,B,R,R,R,R]
(30/50) x (29/49) x (20/48) x (28/47) x (19/46) x (27/45) x (26/44) x (25/43) x (24/42)

Notice that the denominators stay the same but the numerators change order. That is, the probability of each outcome remains the same.

P(E)=⁹C₂ x {[(30!)(20!)]/[(23!)(18!)]}

I hope this is right!

Thank you so much but i dont really understand this part
{[(30!)(20!)]/[(23!)(18!)]} what does that mean exactly (as i am in two unit and havnt seen this before) and were did the 23 and 18 come from? thx

 

[lychnobity]

Thank you so much but i dont really understand this part
{[(30!)(20!)]/[(23!)(18!)]} what does that mean exactly (as i am in two unit and havnt seen this before) and were did the 23 and 18 come from? thx

The exclamation mark, "!" means factorial. The factorial is a way of saying that number times by all the numbers below it. Eg 30! means 30 x 29 x 28 x ...x2 x 1

This would be used where you wanted to find the no. ways you could arrange something in a line without replacement for example. Eg arrange 5 people in a line would be 5 x 4 x 3 x 2 x 1 = 5!

 

[toprun91]

The exclamation mark, "!" means factorial. The factorial is a way of saying that number times by all the numbers below it. Eg 30! means 30 x 29 x 28 x ...x2 x 1

This would be used where you wanted to find the no. ways you could arrange something in a line without replacement for example. Eg arrange 5 people in a line would be 5 x 4 x 3 x 2 x 1 = 5!

OK thanx and what about the 23 and 18 were did they come from

 

[blaze.bluetane]

sorry. I think it should be

P(E)=⁹C₂ x [(30!)(20!)(41!)]/[(23!)(18!)(50!)] anyways
Check out the attachment. That should explain it

bb

 

[toprun91]

sorry. I think it should be

P(E)=⁹C₂ x [(30!)(20!)(41!)]/[(23!)(18!)(50!)] anyways
Check out the attachment. That should explain it

bb

Thankyou