• 0
BMAD

Dentist's agree

Question

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?

0

Share this post


Link to post
Share on other sites

4 answers to this question

  • 0

I'll make these assumptions.
  1. "Effectively treated" means "cured."
    Both terms are used in the OP so I take them to mean the same thing.

  2. Those without plaque cannot be cured of plaque.
    So, off the top, 7 out of 17 people will not be "effectively treated."

  3. "Four out of five dentists agree ... x." means "x has a probability of 0.8."

If we were to treat a representative group of 17 people,

Five would have plaque and gingivitis. They would contribute 5/17 x .8 x .95 effectively treated cases.

Five would have plaque but no gingivitis. They would contibute 5/17 x .8 x .85 effectively treated cases.

Seven would have no plaque. They would contrubute 7/17 x 0 effectively treated cases.

Effective treatment probability of a random person is therefore

p(effective) = 5/17 x .8 x .95 + 5/17 x .8 x .85 + 7/17 x 0 = 7.2/17 = 0.4235.

0

Share this post


Link to post
Share on other sites
  • 0

Do we know the prior probability of having gingivitis?

0

Share this post


Link to post
Share on other sites
  • 0

Oh. assume 50 50 chance

0

Share this post


Link to post
Share on other sites
  • 0

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%

0

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now

  • Recently Browsing   0 members

    No registered users viewing this page.