apoorvk 3 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.

1. Ishaan94

:( I can't solve it, @foolformath HELP.

2. apoorvk

nahii.. ISHAAN, ye naaahhiii ho saktaa!! :p :D

3. leemichaeljh

I can't also.

4. Ishaan94

lol @mr.math @dumbcow

5. apoorvk

@myininaya

6. apoorvk

7. ch2831

should be 1 in 448

8. Ishaan94

How?

9. apoorvk

now explanation will be appreciated. :)

10. apoorvk

am getting stuck somewhere. and i can't untangle my mind.. :/

11. ch2831

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

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

no one's calling for lgbaaaa :( well i dunno this either...

14. Mani_Jha

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

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

right so far mani, and i seem to be seeing it clearer now.

17. apoorvk

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

'OR'

19. Mani_Jha

oh yeah. you're right. Now let me think how to use the given probability ratio.

20. Mani_Jha

@ch2831, where did you get the number 448 from?

21. arcticf0x

The names have been badly chosen :P

22. ch2831

4*4*4*7. Isnt it 448?

23. Mani_Jha

Yeah, it is. Please explain why you chose that number. To be honest, I didn't understand your answer.

24. dumbcow

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

Oh so this is how the probability ratio is used

26. Mani_Jha

Oh...This topic really isn't made for me :=(

27. dumbcow

i believe that is right, the probability you watch is 3 times greater than not watching

28. apoorvk

@dumbcow .. yayy!!!!!!!!!! you did it i guess!!! yeah he took the ratio thing right too, ishaan!

29. apoorvk

@arcticf0x , the names have been *purposefully* chosen. :p

30. Ishaan94

Nice solution :-) #I need to study probability :/