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Posted 28 April 2014 - 01:20 AM
Ten out of 17 people suffer from plaque buildup, but Four out of five dentist agree that the new BMAD formula for mouth rinse will cure 95% of the people with gingivitis of plaque build up and is 85% effective for those who do not have gingivitis. If a random person is selected what is the probability they would be effectively treated of plaque buildup?
Posted 28 April 2014 - 08:52 AM
Do we know the prior probability of having gingivitis?
Vidi vici veni.
Posted 28 April 2014 - 08:46 PM
I think it also depends on what the remaining fifth of dentists think too. e.g. they might think that the BMAD formula is effective on 100% of plaque buildups (case A extreme) or totally ineffective (case B extreme) whether a person has or doesn't have plaque buildup.
case A extreme:
probability that the person has plaque = P(has plaque) = 10/17
P(effectively treated) =
P(BMAD's formula behaves as 4/5 dentists predict)*[P(has gingivitis and is effectively treated) +P(doesnt have gingivitis and is eff. treated)] +
P(BMAD's formula behaves as 1/5 dentists predict)*[P(has gingivitis and is effectively treated) +P(doesnt have gingivitis and is eff. treated)] +
P(BMAD's formula doesnt behave as any of the dentist's predict)*[P(has gingivitis and is effectively treated) +P(doesnt have gingivitis and is eff. treated)]
Another Assumption (the last summand in the above sum is 0)
therefore, P(eff. treated)= 0.8(0.5*0.95 + 0.5*0.85) + 0.2(1) = 0.4(1.8) + 0.2 = 92%
case B extreme:
Under similar assumptions
P(eff. treated)= 0.8(0.5*0.95 + 0.5*0.85) + 0.2(0) = 0.4(1.8) + 0.2 = 72%
Posted 04 May 2014 - 09:18 AM Best Answer
Vidi vici veni.
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