Imagine that you are asked to evaluate the five-year viability of a new consulting firm, ConsultIng. Based on your prior research, you have established that 20% of similar firms in this area survive for at least five years, with 80% going out of business within this period. However, your research also reveals that 90% of non-surviving firms had asset/liability ratios which were worse than that of ConsultIng, as opposed to 50% of surviving firms. What is the probability that ConsultInc will survive for at least five years?

Probability of Consulting surviving is 0.56

Step-by-step explanation:

The probability of Consulting surviving = (Probability of surviving) / { (Probability of not surviving) + (Probability of surviving) }

Define terms:

Survival based on research (S1) = 20%=0.2

Survival based on asset/liability ratio (S2) = 50%=0.5

Non-survival based on research (F1) = 80%=0.8

Non-survival based on asset/liability ratio (F2) = 100-90=10% = 0.10

Therefore

Probability of survival = (S1*S2) / { (S1*S2) + (F1*F2) }

= (0.2*0.5) / { (0.2*0.5) + (0.8*0.1) }

=0.1 / (0.1 + 0.08)

= 0.1/0.18

= 0.56