#Probability help

91 messages · Page 1 of 1 (latest)

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rare tendon
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Here is the markscheme that makes no sense to me....how can you up your own value of n ?

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Can this be done using a probability tree ?

tame leaf
rare tendon
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I meant to say "make up your own value of n", sorry. So in the question there's two possible ways of doing it, making n=2 or n=5. I don't get how they do that.

tame leaf
rare tendon
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Yes

tame leaf
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And you want the same number of all three colors, right?

rare tendon
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Ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh. So for n=2 it's like saying they added one red ball and then one green ball, right ?

tame leaf
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...no.

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We're looking for possible values of n that enable us to get the same number of balls for all three colors.

rare tendon
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Oh wait yeah lol so we add one red ball and subtract one green ball. Add one red ball to get 5 and subtract one green ball (from two green balls) to get one ?

tame leaf
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...no. We subtract, then add.

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So we're subtracting one red ball and then adding one green ball.

rare tendon
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Oh right.....

tame leaf
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...because we start with 4 red and 3 yellow, and... y'know. 4 - 1 = 3.

rare tendon
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Oh wait i think i understand the syntax of the question now... Is the question saying that red and yellow and green should be the same number ?

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I thought it meant that the number of red balls in bag A = number of red balls in bag B and so on...

tame leaf
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...yes. That's why it says "The probability that bag A now contains an equal number of red, yellow and green balls is p."

rare tendon
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AHhhhhhh..... i see. ooops

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Wow ok this whole question makes so much sense now. Thanks alot !

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Could you by any chance assist me with this other question ?

tame leaf
rare tendon
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I don't know how they got the equation: 3c=0.25

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Oh wait i think i just figured it out.

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I'm getting a bit confused with the equation of independence.

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Which is p(A and B) = P(A)xP(B)

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But how can i do that with a single variable like C because naturally it is independent of A and B since they are games that have come before it

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I can see that they've gotten the equation from doing C=a+b but i'm not too sure how i can get this my best guess is inderpendence but i dont know how to relate it.....

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Oh wait that still doesn't make sense because C is posotive so it won't give 3c when rearranged.

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Yeah im completely lost now

tame leaf
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Okay, wait.

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Did you calculate a, b, and c?

rare tendon
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I got one equation for a,b and c

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I got that a+b=2c+0.15

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from this line here

image.png
tame leaf
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Actually, yeah, you only need c.

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Because it's impossible to score 0 or 1 on one game and sum to 6 with two.

rare tendon
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yeah..

tame leaf
rare tendon
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I wanted to create an equation using probabilities and independence. From this line it basically says that C is independent of a and b. So i thought somehow I could get an equation using independence to get a+b=c. But even if that made sense that equation (once you sub in a+b value) doesn't rearrange to give 3c=0.25

image.png
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Oh somebody gave me the answer to the question lol.

tame leaf
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You don't need a and b.

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You can ignore a and b entirely.

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You just need c.

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Which you already have.

rare tendon
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Yep. We just need another value of a+b so we can make two equations of c equal to eachother. I got told that apparently I had forgotten one of the most important rules of probabilities...they sum to 1. So we can get a+b+c+0.1+0.15 = 1. Then simplify this equation and make this equal to our other equation to find c

tame leaf
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Okay, stop.

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Or, wait.

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Don't stop, necessarily.

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I mistook something.

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Wait.

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Okay, so you're saying you haven't actually found the value of c?

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Okay, look.

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We have P(S < 2) = 2P(S >= 2), right?

rare tendon
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Yeppers

tame leaf
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Now, what's P(S >= 2)?

rare tendon
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c+0.1+0.15 ?

tame leaf
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And what else is it?

rare tendon
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2( c+0.1+0.15) right ?

tame leaf
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No.

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How could it be twice itself?

rare tendon
tame leaf
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Is it possible for S to be neither less than, nor greater than or equal to 2?

rare tendon
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So it would have to be equal to a+b i think ?

rare tendon
tame leaf
rare tendon
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Oh sorry i thought you meant the lower case s. The upper case S must be less than or equal to one as it's a probabiltiy and probabilities sub to 1 ?

tame leaf
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Okay, stop.

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Is it possible for any number to be both less than and greater than or equal to any other number?

rare tendon
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Ohhhh at the same time ? No

tame leaf
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Is it possible for a < b and a >= b to both be true?

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Okay, good.

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Is it possible for a < b and a >= b to both be false?

rare tendon
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Yes as A could potentially be <= B ?

tame leaf
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...then either a < b or a = b which means a >= b.

rare tendon
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Would that not be a<=b

tame leaf
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How can a be both less than and equal to b?

rare tendon
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Well it's not and it's or... a can be equal to b or it can be less than b

tame leaf
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...and if it's less than, then it's less than, and if it's equal to, then it's greater than or equal to.

rare tendon
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Why are you flipping the sign from less than to greater than ?

tame leaf
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I'm not flipping a sign!

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If a = b, then a >= b, true or false?

rare tendon
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False. If it is something it cannot be greater than that something as it is it. It cannot be greater than itself...?

tame leaf
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...you literally just said that it's not an and, it's an or.

rare tendon
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Well it depends how you define the variables...If we know that a=b then we cannot say that a>=b because while it is equal to b how can it be greater than it ? I'm fine with saying a>=b by itself but not saying that a=b and then going onto say that a>=b. It's like saying a=5 and b=5 (a=b) and then saying 5>=5- well yess 5=5 but 5 is not > than 5 ?

tame leaf