Probabilty and Odds?

hi guys,

i was watching a game of lawn balls and the results of the game led me to come up with this question:

In a game of lawn balls:
7 rinks
2 teams per rink.
a total of 14 teams

after the first round of games the teams switch randomly and play another round of games.

every team has played two games each.

Normally at the end of the two games there are 2, maybe 3 teams who have won both games.

What are the odds & the probability that 6 teams have won two games?

I have the below solutions:
Probability: 13/9
Odds: 13:4

But I think I haven't accounted for a value.

thanks!
P

Hello, plato9!

Could you show your work?
Can't help but wonder how you came up with

Quote:

---

i was watching a game of lawn balls and the results of the game
led me to come up with this question:

In a game of lawn balls:
. . 7 rinks
. . 2 teams per rink.
. . a total of 14 teams

After the first round of games the teams switch randomly
. . and play another round of games.

Every team has played two games each.

Normally at the end of the two games there are 2, maybe 3 teams
. . who have won both games.

What are the odds & the probability that 6 teams have won two games?


I have the below solutions:

Probability: 13/9 . . . . 5 out of 4 people have trouble with probability.

Odds: 13:4 . . . . This makes no sense.

But I think I haven't accounted for a value. . What does this mean?

---

hi Soroban,

sorry! a bit of late night miscalculation.
ignore the solutions i gave.
this is what i did (re-did)

New solutions:
Pobability: 1/9
Odds: 1/4

Method
Probability = favorable outcome/total outcomes

There is only one favorable outcome = winning

Total outcomes = 3 (win, lose, tie)

Therefore:
Probability of a team wining first round = 1/3
Probability of the same team wining second round = 1/3

P(a team winning both rounds) = 1/3 . 1/3 = 1/9


Odds
Odds = outcomes for/outcomes against = 1/2

Odds(a team winning both rounds)=1/2.1/2 = 1/4


With the above I have assumed that all teams have an equally matched but in reality that wouldn't be the case

My Notes:
Round 1
Team A vs Team B
Team C vs Team D
Team E vs Team F
Team G vs Team H
Team I vs Team J
Team K vs Team L
Team M vs Team N

Only 6 teams win the first round:
A,C,E,G,I,K

Teams switch randomly and play a second round
Round 2
Team N vs Team B
Team A vs Team D
Team M vs Team F
Team K vs Team H
Team C vs Team J
Team E vs Team L
Team G vs Team I

The same 6 teams who won the first round also win the second round :
A,C,E,G,I,K



Many thanks!
P