manuel and ruben played dominoes 24 times. Ruben has won 16 times. estimate the odds in favor of Manuel's winning the next match.
prob(Ruben winning) = 16/24 = 2/3
prob(Ruben NOT winning) = 1/3
so
prob(Manuel winngin) = 1/3
prob(Man not winning) = 2/3
odds in favour of Manuel winning
= (1/3) : (2/3)
= 1 : 2
To estimate the odds in favor of Manuel's winning the next match, we need to calculate the probability of Manuel winning based on the information given.
The number of times Ruben won is 16 out of a total of 24 games played. Therefore, we can calculate Ruben's winning probability as:
Ruben's winning probability = Number of times Ruben won / Total number of games played
Ruben's winning probability = 16 / 24
Ruben's winning probability = 2/3
Since there are only two players (Manuel and Ruben), Manuel's winning probability can be calculated as:
Manuel's winning probability = 1 - Ruben's winning probability
Manuel's winning probability = 1 - 2/3
Manuel's winning probability = 1/3
So, the odds in favor of Manuel's winning the next match would be:
Odds in favor of Manuel = Manuel's winning probability / Ruben's winning probability
Odds in favor of Manuel = (1/3) / (2/3)
Odds in favor of Manuel = 1/2
Therefore, the odds in favor of Manuel's winning the next match is 1:2 or 1/2.