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apoorvk

  • 2 years ago

Three friends Roger, Djoko and Rafael (:p) went to watch a tournament of tennis on a certain day of the event, when a total of 7 matches were being held (no match-timings coinciding with any other). All the 3 friends can either watch a match or loiter around in the arena with the probability ratio (3:1) On entering the arena, all 3 went their separate ways. Find the probability of none of them having witnessed any particular match together.

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  1. Ishaan94
    • 2 years ago
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    :( I can't solve it, @foolformath HELP.

  2. apoorvk
    • 2 years ago
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    nahii.. ISHAAN, ye naaahhiii ho saktaa!! :p :D

  3. leemichaeljh
    • 2 years ago
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    I can't also.

  4. Ishaan94
    • 2 years ago
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    lol @mr.math @dumbcow

  5. apoorvk
    • 2 years ago
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    @myininaya

  6. apoorvk
    • 2 years ago
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    help myininaya, please!!!

  7. ch2831
    • 2 years ago
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    should be 1 in 448

  8. Ishaan94
    • 2 years ago
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    How?

  9. apoorvk
    • 2 years ago
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    now explanation will be appreciated. :)

  10. apoorvk
    • 2 years ago
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    am getting stuck somewhere. and i can't untangle my mind.. :/

  11. ch2831
    • 2 years ago
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    Change my answer. 27 in 448 chance that they will all meet, 136 in 448 chance that a and b will meet, 136 in 448 chance that b and c will meet, 136 in 448 chance that a and c will meet. 3*136- 2*27= 354 in 448 chance that they will meet at all. Therefore 94 in 448 (you can simplify it) chance that they will not meet at all.

  12. Ishaan94
    • 2 years ago
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    Timings of the match doesn't coincide with eachother, so when they enter the stadium they must have only one match to watch, lets they don't watch it together. So, there must be three cases either one of them watches the match or two or none. \[\text{_________________________________________________________________________________}\]Now help me do the math.

  13. lgbasallote
    • 2 years ago
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    no one's calling for lgbaaaa :( well i dunno this either...

  14. Mani_Jha
    • 2 years ago
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    For each of the three persons, there are two choices - watch the match or not, for each of the seven matches. So, total no of ways in which each one completes the day is 2X2X2..=2^7. Is this right so far?

  15. Mani_Jha
    • 2 years ago
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    The total no of choices for the 3 people would be 3X2^7. Atleast I found out the denominator of my fraction..:P

  16. apoorvk
    • 2 years ago
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    right so far mani, and i seem to be seeing it clearer now.

  17. apoorvk
    • 2 years ago
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    unhnn....the choices for the three would get multiplied rendering your denominator 2^21, since it is an 'OR' case, where each member may watch a match or not, and each person's choice being an independent event.

  18. apoorvk
    • 2 years ago
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    'OR'

  19. Mani_Jha
    • 2 years ago
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    oh yeah. you're right. Now let me think how to use the given probability ratio.

  20. Mani_Jha
    • 2 years ago
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    @ch2831, where did you get the number 448 from?

  21. arcticf0x
    • 2 years ago
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    The names have been badly chosen :P

  22. ch2831
    • 2 years ago
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    4*4*4*7. Isnt it 448?

  23. Mani_Jha
    • 2 years ago
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    Yeah, it is. Please explain why you chose that number. To be honest, I didn't understand your answer.

  24. dumbcow
    • 2 years ago
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    hmm i'm getting a really small probability here --> (5/32)^7 each match is an independent event so you would multiply the probabilities hence raising to 7th power each match has 4 possiblilties None watch: --> (1/4)^3 = 1/64 1 watches: --> 3*(3/4)*(1/4)^2 = 9/64 2 watches --> 3*(3/4)^2*(1/4) = 27/64 All watch --> (3/4)^3 = 27/64 so probability less than 2 watch any given match is 10/64 = 5/32

  25. Ishaan94
    • 2 years ago
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    Oh so this is how the probability ratio is used

  26. Mani_Jha
    • 2 years ago
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    Oh...This topic really isn't made for me :=(

  27. dumbcow
    • 2 years ago
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    i believe that is right, the probability you watch is 3 times greater than not watching

  28. apoorvk
    • 2 years ago
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    @dumbcow .. yayy!!!!!!!!!! you did it i guess!!! yeah he took the ratio thing right too, ishaan!

  29. apoorvk
    • 2 years ago
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    @arcticf0x , the names have been *purposefully* chosen. :p

  30. Ishaan94
    • 2 years ago
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    Nice solution :-) #I need to study probability :/

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