## Mitul Group Title Probability of A winning the race is 4/5 and probabilty of B winning the race is 5/6. find the probability that neither wins... one year ago one year ago

1. Yahoo! Group Title

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2. Mitul Group Title

not possible @Yahoo! 1-4/5-5/6 is negative...

3. Yahoo! Group Title

i think the answer will be 0

4. Mitul Group Title

no cannot be....the event has occured....its not an impossible event...

5. Yahoo! Group Title

u see there are only two chances either A will win or B will

(1-4/5)(1-5/6)

7. Mitul Group Title

that can be one case but i nvr said that only A and B are playing.....

wait these are not mutually exclusive events

oh ok gotcha

10. lgbasallote Group Title

uhhh this is just one event right?

11. Mitul Group Title

yeah...event that neither wins...

12. lgbasallote Group Title

yahoo's solution should've been right...

13. lgbasallote Group Title

also this doesnt make sense... 4/5 + 5/6 = 49/30

14. lgbasallote Group Title

the total probability should be less or equal to 1

P(both winning) = 4/5 * 5/6 P(both not winning) = 1- 4/5 * 5/6

16. apple_pi Group Title

draw a probability tree. Remember as we go along we multiply the values

17. lgbasallote Group Title

18. lgbasallote Group Title

what you did is probability that NOT both will win

19. waterineyes Group Title

$P(A \; and \;B \;win) = P(A) \times P(B)$ subtract it from 1 I think..

oh im wrong again @lgbasallote :'(

21. Mitul Group Title

@waterineyes u just did what @rsadhvika did...

22. lgbasallote Group Title

there must be a silly trick to this :/

23. waterineyes Group Title

Subtract them from 1 each and then add them..

24. lgbasallote Group Title

we're thinking too complex...we need to open our brains to the possibilities :/

25. lgbasallote Group Title

i really dont think this is one event

26. lgbasallote Group Title

could you post the whole question?/

27. Mitul Group Title

yup @lgbasallote there are more than one case to this problem

28. lgbasallote Group Title

hmm i knew it =_=

29. Mitul Group Title

this is the whole question @lgbasallote

30. apple_pi Group Title

um, tried my solution?

31. lgbasallote Group Title

the probabilities dont add up to less than or equal to 1

32. Mitul Group Title

33. lgbasallote Group Title

i think what @rsadhvika first posted should work then...

34. waterineyes Group Title

$P(nor\; A) = \frac{1}{5}$ $P(nor \; B) = \frac{1}{6}$ $P(Neither \; A \; nor \;B) = P(nor \; A) + P(nor \; B)$

35. apple_pi Group Title

THINK SIMPLE! PROBABILITY TREE!

36. lgbasallote Group Title

Case I Probability A wont win is 1 - 4/5 = 1/5 Case II probability B wont win is 1 - 5/6 = 1/6 so the probability both wont win is 1/6 x 1/5 = 1/30

37. lgbasallote Group Title

uhh should it be +

38. waterineyes Group Title

Sorry there will come multiplication..

39. Mitul Group Title

this is not the question: Solution: the first case is when only A and B are playing the second case is that there are other players

40. lgbasallote Group Title

uhh can you post the WHOLE question with all these cases?

41. lgbasallote Group Title

no paraphrasing...the exact one...

42. waterineyes Group Title

I think we are making it complicated.. There is one and one case only..

43. Mitul Group Title

@lgbasallote my qestion is perfect....the above is the solution which i gave for two cases....we need to consider both the probabilities

44. lgbasallote Group Title

you're suddenly giving situations...so i think what you originally posted isnt the full question

45. Mitul Group Title

Case -1 1-P(A)-P(B) Case-2...possibility that there are other playersss p(A and B cannot winwin)=1-[4/5+5/6-4/5*5/6]

46. apple_pi Group Title

4/5 -> A will win (B cannot win) 1/5 -> A will not win (B still can) 5/6 -> B will win 1/6 -> B will not win (Neither A or B wins) [What you want] If you take a look at my probability tree, you will see what I mean. Remember you multiply the values as you go along. So, YOUR ANSWER -> 1/6 * 1/5 = 1/30

47. telliott99 Group Title

The example violates basic probability rules. If only one can win then P(A) + P(B) <= 1

48. apple_pi Group Title

@telliott99, remember there are others in this 'race' or whatever it is.