A university-based research group is simultaneously bidding forthe rights to und

Question

A university-based research group is simultaneously bidding forthe 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 nexttwo 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: g) probability of the group failing to deliver any fully operational system in the nexttwo years, [1596] ) probability of the group delivering exactly one fully operational system in the next two years. [1596]

Explanation / Answer

P( failing to deliver any) =[ P( not selected for 1) + P( fail/selected) ] *[P( not selected for 2) + P( fail/selected)] = (0.6+0.22)*(0.7+0.135) = 0.6847

P( Exactly one) = 1- P( both)-P( none) = 1 - 0.6847-0.0297 = 0.2856

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