## apoorvk Group Title 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. 2 years ago 2 years ago

1. Ishaan94 Group Title

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

2. apoorvk Group Title

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

3. leemichaeljh Group Title

I can't also.

4. Ishaan94 Group Title

lol @mr.math @dumbcow

5. apoorvk Group Title

@myininaya

6. apoorvk Group Title

7. ch2831 Group Title

should be 1 in 448

8. Ishaan94 Group Title

How?

9. apoorvk Group Title

now explanation will be appreciated. :)

10. apoorvk Group Title

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

11. ch2831 Group Title

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 Group Title

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 Group Title

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

14. Mani_Jha Group Title

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 Group Title

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 Group Title

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

17. apoorvk Group Title

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 Group Title

'OR'

19. Mani_Jha Group Title

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

20. Mani_Jha Group Title

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

21. arcticf0x Group Title

The names have been badly chosen :P

22. ch2831 Group Title

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

23. Mani_Jha Group Title

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

24. dumbcow Group Title

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 Group Title

Oh so this is how the probability ratio is used

26. Mani_Jha Group Title

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

27. dumbcow Group Title

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

28. apoorvk Group Title

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

29. apoorvk Group Title

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

30. Ishaan94 Group Title

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