In the 2009 Season, the Toronto Blue Jays finished the season with a record of 75-87. In 47 of those games, both the offense and defense performed adequately, and in 42 of them, neither the offense nor the defense performed adequately. Of the remaining 73 games, only the offense per performed adequately 37 times and only the defense performed adequately in the other 36.
When only the defense performed adequately, there was a 4/9 probability of winning, while they won 12 of the 37 games that only the offense performed adequately.
Required:
a) What is the probability that the Blue Jays won given that neither the offense nor defense performed adequately?
b) What is the probability that both the offense and defense performed adequately given that that Blue Jays won?
c) What is the probability that both the offense and defense performed adequately given that that Blue Jays lost?
d) What is the probability that neither the offense nor defense performed adequately given that that Blue Jays lost?
e) What is the probability that the Blue Jays lost and only the offense performed adequately?
f) What is the probability that the Blue Jays lost given that only the defense performed adequately?
g) What is the probability that only the offense performed adequately given that that Blue Jays won?