Question

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.

Answer 1

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

Answer 2

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

Answer 3

I can't also.

Answer 4

lol

@mr.math @dumbcow

Answer 5

@myininaya

Answer 6

help myininaya, please!!!

Answer 7

should be 1 in 448

Answer 8

How?

Answer 9

now explanation will be appreciated. :)

Answer 10

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

Answer 11

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.

Answer 12

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.

Answer 13

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

Answer 14

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?

Answer 15

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

Answer 16

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

Answer 17

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.

Answer 18

'OR'

Answer 19

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

Answer 20

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

Answer 21

The names have been badly chosen :P

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

Oh so this is how the probability ratio is used

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

Nice solution :-)

#I need to study probability :/