A university-based research group is simultaneously bidding for the rights to un

Question

A university-based research group is simultaneously bidding for the rights to undertake a cryptography research project for the Home Office, and an automated health delivery system for the National Health Service (NHS). The group’s researh diretor estiates that the proaility of the group being selected to undertake the cryptography project is 40%, and if they are selected for the project, the group has a 45% chance of delivering an operational cryptography system within the next two years. As for the automated health delivery system, the research director believes that the group has a 30% chance of being selected, and if the group is selected for the project, the group has a 55% chance of delivering a fully operational automated health delivery system for the NHS within the following two years.

Calculate each of the following probabilities:

c) probability of successfully delivering both a fully operational cryptography system for the Home Office and a fully operational automated health delivery system for the NHS in the next two years

d) probability of the group successfully delivering at least one fully operational system in the next two years,

Explanation / Answer

C) Probability of both = P( selected for 1st)* P( successful/ selected for first) * P( selected for 2nd)* P( successful/ selected for 2nd) = 0.40*0.45 * 0.30*0.55 = 0.0297

d) probability of the group successfully delivering at least one fully operational system in the next two years, = P( selected for 1st)* P( successful/ selected for first) + P( selected for 2nd)* P( successful/ selected for 2nd) =  0.40*0.45 + 0.30*0.55 = 0.18+0.165=0.345

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