Urn A has 16 white and 10 red balls. Urn B has 2 white and 9 red balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a red ball is selected.
What is the probability that the coin landed heads?

- anonymous

- katieb

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- anonymous

- is3535

9 didve by 2=

- anonymous

how'd you get 9/2? @is3535

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## More answers

- is3535

Urn B has 2 white and 9 red balls

- anonymous

9/2 is 4.5 @is3535

- is3535

that your answer

- anonymous

4.5?

- anonymous

4.5? its asking the probability? @is3535

- anonymous

- is3535

oh im sry it will be 9

- is3535

whic is biger 9 or 2

- anonymous

9

- is3535

yea

- is3535

9 is your answer

- anonymous

how? @is3535

- is3535

Urn B has 2 white and 9 red balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a red ball is selected.
What is the probability that the coin landed head,

- anonymous

are we doing some ratio??? or like....

- is3535

|dw:1444156898622:dw|

- anonymous

its just saying, Suppose that a red ball is selected. What is the probability that the coin landed heads? @Leong

- anonymous

4.5 :v you take 9 divide for 2, like you got less ball mean less chance.

- anonymous

- anonymous

- Pulsified333

Probability can not be more than 1

- anonymous

okay :v then if not one we should do some ratio here: 10 over 16, means that 0.625 chance that the A get to choose :v

- anonymous

i don't think thats right @Leong

- anonymous

- BAdhi

This involves conditional probability and total probability theorem @vzforever are you familiar with them?

- anonymous

yes @BAdhi

- BAdhi

can you show me the given information written as the notation used in probability such as p(A) , p(B) etc

- anonymous

i don't understand @BAdhi

- BAdhi

can you write down the given information in the mathematical notation? for example
probability of choosing A => P(A)

- anonymous

Pr(A)= 1/2 Pr(B)= 1/2 @BAdhi

- anonymous

what next? @BAdhi

- BAdhi

what about the probability of getting a red ball given that we have choosen A? can you show it in the notation?

- anonymous

Pr(AR)=10/26

- BAdhi

umm, by P(AR) you mean \(P(A \cap R)\) ?

- anonymous

no its 10/42 @BAdhi

- BAdhi

10/42 is the probability of choosing a red ball out of all the balls..
but you see, since its already given that A has been choosen the amount of balls are reduced to 26.
And i still need the answer to the previous question @vzforever

- anonymous

whats ur previous question? @BAdhi

- BAdhi

what do you mean by P(AR).. from what ive learned no such notation is used in prbability either it has to be \(P(A\cap R) , P(A\cup R), P(A|R)\) ??

- anonymous

yes ur right

- anonymous

what u said before was correct

- BAdhi

ok.. what about the notation.. arent you going to answer my question?

- anonymous

i said yes its (P(A \cap R)\)

- BAdhi

\(P(A\cap R)\) means the probility of choosing a red ball and choosing A
in here event -> choosing A and choosing red ball has still not occured
but what i asked was, probability of choosing a Red ball given that A is choosen.
in here A has already being chosen

- BAdhi

so the correct notation is \(P(R | A)\)

- anonymous

ok

- BAdhi

similarly you can find P(B), P(R|B), P(W|B), P(W|A)
so since the event -> turning head and the event -> choosing A are both same, what they are asking is,
P(A|R)

- anonymous

ok so is it (1/2)/(10/42)

- anonymous

which is 5/42

- BAdhi

so what you are saying is,
\(P(A|R) = P(R)\times P(A)\) ??

- anonymous

can you explain to me? i need to get this done.

- anonymous

- BAdhi

Its normal to get confused with the difference between \(P(A\cap R)\) and \(P(R|A)\)
so I recommend you to read and look more into the explanation ive given in the previous post
The definition of the conditional probability is,
\(P(R|A) = \frac{P(R\cap A)}{P(A)}\)
since P(R|A) and P(A) are known, you can find \(P(R\cap A)\)
since what they are asking is P(A|R) ,
\(P(A|R) =\frac{P(A\cap R)}{P(R)} \)
can \(P(A\cap R)\) is obtained in the previous step and hope you know how to find P(R)

- anonymous

ok so what do i do to solve this problem

- anonymous

we haven't even gotten there yet

- anonymous

- anonymous

@BAdhi can we do the problem?

- BAdhi

thats what im trying to do the whole time.. i dont wanna give you the answer straight forward, since itll be pretty useless.
as a guidance let me state this, you have to find the values of the following variables from the given information straight forward
P(A), P(R|A), P(R)
with use of conditional probability definition (which ive given above) you have to find
\(P(A\cap R)\)
after that find P(A|R) with use of the same conditional probability definition (which is also given previously)
what they are asking is the value of P(A|R)

- anonymous

ok

- anonymous

can u explain with numbers

- BAdhi

it is really important to know the difference between P(A|R) and \(P(A \cap R) \) since , as you can see even in this problem they are applied so close together in problems
Are you clear with the difference between them?

- BAdhi

first give me what youve tried pls after that ill give the answer

- anonymous

110/299 and 299/462 are the answers I've gotten and neither are right. obviously i need help cause idk what I'm doing. and I've made a tree

- anonymous

- anonymous

- BAdhi

can you show the steps too.. that would be a good starter

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