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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: a weaponized ikea chair on May 29, 2020, 11:45:18 am

Title: help with prob question
Post by: a weaponized ikea chair on May 29, 2020, 11:45:18 am

thanks   :)

Title: Re: help with prob question
Post by: Sine on May 29, 2020, 11:47:06 am

Quote from: a weaponized ikea chair on May 29, 2020, 11:45:18 am

thanks   :)

What aspect of the question is difficult for you?

What working out have you done so far?

Title: Re: help with prob question
Post by: a weaponized ikea chair on May 29, 2020, 11:48:40 am

Quote from: Sine on May 29, 2020, 11:47:06 am

What aspect of the question is difficult for you?

What working out have you done so far?

I have tried using a two-way table but never get an answer that is one of the options.

Title: Re: help with prob question
Post by: colline on May 29, 2020, 12:32:55 pm

Quote from: a weaponized ikea chair on May 29, 2020, 11:48:40 am

I have tried using a two-way table but never get an answer that is one of the options.

In addition to a two-way table, see how you can use the information that the two are independent.

Find Pr(A) and Pr(B) first. Since they are independent, then Pr(A) * Pr(B) = Pr(A and B). Hope this helps! :)

Title: Re: help with prob question
Post by: a weaponized ikea chair on May 29, 2020, 01:54:54 pm

Quote from: colline on May 29, 2020, 12:32:55 pm

In addition to a two-way table, see how you can use the information that the two are independent.

Find Pr(A) and Pr(B) first. Since they are independent, then Pr(A) * Pr(B) = Pr(A and B). Hope this helps! :)

Thank you! I was now able to figure it out!

Quick question: if they were not independent, rather they were dependant, could you use the rule Pr(A) * Pr(B) = Pr(A and B)?

Title: Re: help with prob question
Post by: colline on May 29, 2020, 03:23:54 pm

Quote from: a weaponized ikea chair on May 29, 2020, 01:54:54 pm

Thank you! I was now able to figure it out!

Quick question: if they were not independent, rather they were dependant, could you use the rule Pr(A) * Pr(B) = Pr(A and B)?

The formula only applies if they are independent, so no.

Edit (if you want to know why):

Independent suggests the two events A and B literally do not affect each other in any way. So for example the probability of A happening given that B is true [i.e. Pr(A|B)] is no different to the probability of just A [i.e. Pr(A)]. So we can say that:
Pr(A|B) = Pr(A) when the two are independent.

And we know that Pr(A|B) = Pr(A and B) / Pr(B). Using the independence formula, Pr(A and B) = Pr(A) * Pr (B), so we can rewrite it as Pr(A) * Pr(B) / Pr(B). The Pr(B) cancels out and you are left with Pr(A|B) = Pr(A) when A and B are independent.

I hope that makes sense!