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In a typical year, California Consulting responds to 10 requests for proposals (RFPs) in hopes of...

In a typical year, California Consulting responds to 10 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 0.4.

  1. What is the probability of exactly 4 successful RFPs?

  1. What is the probability of at least 3 but not more than 6 successful RFPs?
  1. One particular RFP has been submitted for a large research project. Initially California Coonsulting felt that there was a 50-50 chance of getting the project; however, the agency to which the bid was submitted has subsequently asked for additional information on the bid. Past experience indicates that on 80% of the successful bids and 30% of the unsuccessful bid, the agency requested additional information. Compute the posterior probability that the bid will be successful given that a request for additional information has been received.
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