In any given season, a soccer team plays 65% of their games at home. When the team plays at home, they win 83% of their games. When they play away from home, they win 26% of their games. The team plays one game. If the team does not win the game, find the probability that the game was played at home.

29.9%

Step-by-step explanation:

We have that 65% of the games are at home, therefore 35% (100 - 65) are away from home.

We have that at home, they win 83% of the matches, therefore 17% (100 - 83) lose them.

Also away from home they win 26% of the games, which means that 74% (100 - 26) lose them.

We are asked that if the team does not win the game, find the probability that the game was played at home.

Then the favorable cases would be that he has played at home and that he has lost, that is, 65% (home games) and 17% (lost at home), the probability would be:

65% * 17% = 0.1105

Now, the probability that he loses, either at home or away from home, would be the sum of the previous probability plus when he loses away, which would be 35% of the away games, the 74% who are the losers, is say:

74% * 35% = 0.259

Therefore the probability would be:

0.1105 / (0.259 + 0.1105) = 0.299

Which means 29.9%