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 projectforthe Home Office, and an automated health delivery systemfor 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 forthe project, the group has a 55% chance of ysystemforthe NHS within the following two years. Calculate each of the following probabilities: d) probability of the group successfully delivering at least one fully operational system in the nexttwo years, [10%] e) probability of the group failing to delivera fully operational cryptography system forthe Home Office in the nexttwo years, [10%] f) probability of the group failing to delivera fully operational automated health delivery system forthe NHS in the next two years, [10%]

Explanation / Answer

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

e) P( failing to deliver crypto) = P(selected for crypto) * P( fail/selected) = 0.40 *(1-0.45) = 0.22

f)  P( failing to deliver home automation) = P(selected for hoe automation) * P( fail/selected) = 0.30 *(1-0.55) = 0.135

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