The completion time of a construction project depends on whether the carpenters, plumbers or electricians working on the project go on strike. If carpenters alone go on a strike, the probability of a delay is 55%. For plumbers and electricians alone, these probabilities are 45% and 25%, respectively. The strike of two or more of these trades simultaneously results in a delay 85% of the time. There is a 20% chance that each of these trades will go on strike. There is a 4% chance that exactly any two of the trades go on strike and it is equally likely to be any two of the three (i.e., the probability that plumbers and electricians go on strike, but not carpenters is 4%, etc). Finally, there is 2% chance that all three trades will go on strike.

a) What is the probability that a delay happens in the completion of this construction project?

b) If a delay happens, what is the probability that the carpenters alone went on strike?

c) If a delay happens, what is the probability that two or more trades went on strike?