Math *Questions* Involving Probablity

[darshanpatel]

Homework Statement

1) How many times must you roll two six-sided dice for there to be at least a 50% chance that you roll two 6's at least once?2) It is estimated that 5.9% of Americans have diabetes. Suppose a medical lab uses a test for diabetes that 98% accurate for people who have the disease and 95% accurate for the people who do not have it. Find the conditional probability that a randomly selected person actually has diabetes given that the lab test says they have it.

Homework Equations

-None-

The Attempt at a Solution

Question One:

Work: chance of rolling a six(dice one) x chance of rolling a six(dice two) x one half

1/6 x 1/6 x 1/2 = 1/72

72 rolls?

Question Two:

Work:

P(accurate) x (accurate|don't have diabetes) - P(accurate) x (accurate|have diabetes)
(.95 x .941)-(.98 x .059)= .89395-.83163 = about 5.782% ?

 

[jedishrfu]

q1: mathematicians look at this problem in reverse and instead ask what's the probability of not getting two sixes in a row and then multiply it over and over until they get to the 50% mark and the number of times they multiplied will be the number of rolls needed.

q2: is a a bayesian conditional probability question, you need the bayes eqn to compute it:

p(A given B) = p(B given A) * p(A) / p(B) or succinctly p(A|B)=p(B|A)p(A)/p(B)

where A= prob of having diabetes and B=prob of positive test

 

[Villyer]

My approach to problem two was to set an arbitrary number of people in the population (say 1 million) and then figure out the number of people who A) have the disease and get a positive test result and then B) don't have the disease, but still get a positive result.
Then the answer is A/(A+B), which was ~55%I only approached the problem this way because I'm not familiar with bayesian equation that jedishrufu mentioned.

 

[jedishrfu]

Your answer of 5.78% is close to mine of 5.89%

 

[Ray Vickson]

Homework Statement

1) How many times must you roll two six-sided dice for there to be at least a 50% chance that you roll two 6's at least once?


2) It is estimated that 5.9% of Americans have diabetes. Suppose a medical lab uses a test for diabetes that 98% accurate for people who have the disease and 95% accurate for the people who do not have it. Find the conditional probability that a randomly selected person actually has diabetes given that the lab test says they have it.

Homework Equations

-None-

The Attempt at a Solution

Question One:

Work: chance of rolling a six(dice one) x chance of rolling a six(dice two) x one half

1/6 x 1/6 x 1/2 = 1/72

72 rolls?

Question Two:

Work:

P(accurate) x (accurate|don't have diabetes) - P(accurate) x (accurate|have diabetes)
(.95 x .941)-(.98 x .059)= .89395-.83163 = about 5.782% ?

Answer for 1 is n = 25. Answer for 2 is 5782/10487 ≈ 0.55, or about 55%.

RGV