Question

1. California Consulting, LLC is a consulting business operated by Mr. Williams and one of his colleagues. In a typical year, California Consulting responds to 12 requests for proposals (RFPs) in hopes of obtaining business. Each RFP results in either a ‘success’ (California Consulting is awarded the contract) or a ‘failure’ (California Consulting does not win the business). Assume that the outcomes follow the binomial distribution with the probability of success equal to 0.3.

1. What is the probability of exactly 5 successful RFPs?

2. What is the probability of at least 2 but not more than 6 successful RFPs?

One particular RFP has been submitted for a large research project. I initially felt that there was a 50-50 chance of getting the project; however, the agency to which the bid was submitted as subsequently asked for additional information on the bid. Past experience indicates that on 70% of the successful bids and 40% of the unsuccessful bid, the agency requested additional information.

3. Compute the posterior probability that the bid will be successful given that a request for additional information has been received.

Answer 1

Answer:

a)

Given,

n = 12

p = 0.3

P(X = 5) = 12C5 * 0.3^5 * 0.7^(12-5)

= 792*0.0002

= 0.1584

P(X = 5) = 0.1584

b)

P(2 <= X <= 6)

= P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 12C2*0.3^2*0.7^10 + 12C3*0.3^3*0.7^9 + 12C4*0.3^4*0.7^8 + 12C5*0.3^5*0.7^7 + 12C6*0.3^6*0.7^6

= 0.1678 + 0.2397 + 0.2311 + 0.1585 + 0.0792

P(2 <= X <= 6) = 0.8763

c)

Let us consider,

P(s|r) = P(r|s)*P(s) / P(r)

= 0.70 * 0.50 / (0.5(0.70 + 0.40))

= 0.35/0.55

= 0.6364