Question

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?

Answer 1

To find the probability of ConsultIng surviving for at least five years, we can use conditional probability. Given that 20% of similar firms survive, with 90% of non-surviving firms having worse asset/liability ratios than ConsultIng, the probability is approximately 12.2%.

Step-by-step explanation:

To find the probability that ConsultIng will survive for at least five years, we can use conditional probability. Let A be the event that a consulting firm survives for at least five years, and B be the event that the firm has a better asset/liability ratio than the non-surviving firms. We are given that P(A) = 0.20 (20% of similar firms survive), P(B|A) = 0.50 (50% of surviving firms have better ratios), and P(B|A') = 0.90 (90% of non-surviving firms have worse ratios). To find P(A|B), we can use Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / (P(B|A) * P(A) + P(B|A') * P(A'))

P(A|B) = (0.50 * 0.20) / (0.50 * 0.20 + 0.90 * 0.80)

P(A|B) = 0.10 / (0.10 + 0.72)

P(A|B) = 0.10 / 0.82

P(A|B) ≈ 0.122

Therefore, the probability that ConsultIng will survive for at least five years, given that it has a better asset/liability ratio than the non-surviving firms, is approximately 0.122 or 12.2%.

Answer 2

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