Problem 1f The Venture Capitalist (Bernoulli & Binomial Distributions] A venture

Question

Problem 1f The Venture Capitalist (Bernoulli & Binomial Distributions] A venture capitalist (VC) decided to set aside $50M for next year to invest equally among 10 new- venture firms in the risky-technology sector that are seeking additional equity capital. Historically, one out of 20 investments are successful. The others either fail or join the ranks o (companies that are barely surviving and are thus not attractive to other buyers). f the "living dead" If the VC invests $5M each in 10 new-venture firms using the same selection criteria, then... A. B. C. What is the probability that none of the investments succeed? What is the probability that at least one investment succeeds? Assuming that one investment is successful with the above "p" (at a minimum), what return would be required from the company receiving the investment capital if the VC expects to double the $50M invested in the portfolio of companies? D. If only 1 out of 20 investments is successful, what is the minimum number of investments the VC must make to ensure at least 78.5% probability of 1 or more successes?

Explanation / Answer

here p=probability of successful investment=1/20=0.05

here we use binomial distribution with parameter n=10 and p=0.05 and for Binomial distribution ,

P(X=r)=nCrpr(1-p)n-r  

(A)P(non of succeed)= P(X=0)=0.3585 ( using ms-excel=BINOMDIST(0,20,0.05,0))

(B)P(atleast one succeed)=P(X>=1)=1-P(X<1=1-P(X=0)=1-0.3585=0.6415

(D) here n=30 and p=0.05, we get required answer as

1-P(X=0)=0.785

n P(X=0) P(at least 1) 20 0.358485922 0.641514078 21 0.340561626 0.659438374 22 0.323533545 0.676466455 23 0.307356868 0.692643132 24 0.291989024 0.708010976 25 0.277389573 0.722610427 26 0.263520094 0.736479906 27 0.25034409 0.74965591 28 0.237826885 0.762173115 29 0.225935541 0.774064459 30 0.214638764 0.785361236 31 0.203906826 0.796093174 32 0.193711484 0.806288516

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