It is known that 28% of clients of an investment firm have invested in derivatives, and the rest have not. Following a downturn in the economy, 95% of the clients who invested in derivatives are bankrupted, while only 15% of the clients who did not invest in derivatives are bankrupted.
a) If you know that a randomly chosen client is bankrupt, what is the probability that they invested in derivatives?
b) What is the probability that a randomly chosen client is not bankrupt and did not invest in derivatives?
c) What is the probability that a randomly chosen client is not bankrupt or did not invest in derivatives?