## anonymous one year ago 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?

1. anonymous

@is3535

2. is3535

9 didve by 2=

3. anonymous

how'd you get 9/2? @is3535

4. is3535

Urn B has 2 white and 9 red balls

5. anonymous

9/2 is 4.5 @is3535

6. is3535

7. anonymous

4.5?

8. anonymous

4.5? its asking the probability? @is3535

9. anonymous

@Leong @YoloShroom

10. is3535

oh im sry it will be 9

11. is3535

whic is biger 9 or 2

12. anonymous

9

13. is3535

yea

14. is3535

15. anonymous

how? @is3535

16. 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,

17. anonymous

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

18. is3535

|dw:1444156898622:dw|

19. anonymous

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

20. anonymous

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

21. anonymous

@dan815

22. anonymous

@Shalante

23. Pulsified333

Probability can not be more than 1

24. 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

25. anonymous

i don't think thats right @Leong

26. anonymous

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

28. anonymous

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

30. anonymous

i don't understand @BAdhi

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

32. anonymous

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

33. anonymous

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

35. anonymous

Pr(AR)=10/26

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

37. anonymous

no its 10/42 @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

39. anonymous

whats ur previous question? @BAdhi

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

41. anonymous

yes ur right

42. anonymous

what u said before was correct

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

44. anonymous

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

$$P(A\cap R)$$ 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

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

47. anonymous

ok

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)

49. anonymous

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

50. anonymous

which is 5/42

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

52. anonymous

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

53. anonymous

@kropot72

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)

55. anonymous

ok so what do i do to solve this problem

56. anonymous

we haven't even gotten there yet

57. anonymous

@TQKMB

58. anonymous

@BAdhi can we do the problem?

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)

60. anonymous

ok

61. anonymous

can u explain with numbers

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?

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

64. 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

65. anonymous

66. anonymous

@dan815