What was the probability of the Roosters winning their last game at home?

[Bushy]

The Roosters know that they will win 80% of their home matches and 40% of their away matches. This season’s fixture has the Roosters playing 55% of their games at home. Given that the Roosters won their last game, what was the probability that it was played at home? To find the probability of winning = 0.8x.55+0.4x0.45 = 0.62

To find if it was played at home 'given' a win then = the intersection of the two / 0.62

 

[Doffy]

Yes it is correct.
In this case, the conditional probability can be equated as:
$$\frac{P(winning-at-home)}{P(winning)}$$.