Question

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?

Answer 1

@is3535

Answer 2

9 didve by 2=

Answer 3

how'd you get 9/2? @is3535

Answer 4

Urn B has 2 white and 9 red balls

Answer 5

9/2 is 4.5 @is3535

Answer 6

that your answer

Answer 7

4.5?

Answer 8

4.5? its asking the probability? @is3535

Answer 9

@Leong @YoloShroom

Answer 10

oh im sry it will be 9

Answer 11

whic is biger 9 or 2

Answer 12

9

Answer 13

yea

Answer 14

9 is your answer

Answer 15

how? @is3535

Answer 16

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,

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

@dan815

Answer 21

@Shalante

Answer 22

Probability can not be more than 1

Answer 23

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

Answer 24

i don't think thats right @Leong

Answer 25

@BAdhi

Answer 26

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

Answer 27

yes @BAdhi

Answer 28

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

Answer 29

i don't understand @BAdhi

Answer 30

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

Answer 31

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

Answer 32

what next? @BAdhi

Answer 33

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

Answer 34

Pr(AR)=10/26

Answer 35

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

Answer 36

no its 10/42 @BAdhi

Answer 37

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

Answer 38

whats ur previous question? @BAdhi

Answer 39

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

Answer 40

yes ur right

Answer 41

what u said before was correct

Answer 42

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

Answer 43

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

Answer 44

\(P(A\cap R)\) 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

Answer 45

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

Answer 46

ok

Answer 47

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)

Answer 48

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

Answer 49

which is 5/42

Answer 50

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

Answer 51

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

Answer 52

@kropot72

Answer 53

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)

Answer 54

ok so what do i do to solve this problem

Answer 55

we haven't even gotten there yet

Answer 56

@TQKMB

Answer 57

@BAdhi can we do the problem?

Answer 58

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)

Answer 59

ok

Answer 60

can u explain with numbers

Answer 61

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?

Answer 62

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

Answer 63

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

Answer 64

@BAdhi

Answer 65

@dan815