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# Dentist's agree

### #1

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?

### #2

Posted 28 April 2014 - 08:52 AM

Do we know the prior probability of having gingivitis?

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #3

Posted 28 April 2014 - 02:06 PM

Oh. assume 50 50 chance

### #4

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%

### #5

Posted 04 May 2014 - 09:18 AM Best Answer

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

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