Math *Questions* Involving Probablity

  • Thread starter darshanpatel
  • Start date
In summary, it is possible to find the conditional probability that a randomly selected person actually has diabetes given that the lab test says they have it by first setting a number of people in the population and calculating the number of people who have the disease and get a positive test result and then the number of people who don't have the disease but still get a positive test result.
  • #1
darshanpatel
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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% ?
 
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  • #2
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
 
  • #3
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.
 
  • #5
darshanpatel said:

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
 

1. What is probability and how is it calculated?

Probability is a measure of the likelihood of an event occurring. It is calculated by dividing the number of desired outcomes by the total number of possible outcomes.

2. What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes all outcomes are equally likely. Experimental probability is based on actual data from repeated trials and can vary due to chance.

3. How do you calculate the probability of independent events?

The probability of independent events is calculated by multiplying the individual probabilities of each event occurring.

4. What is the difference between dependent and independent events?

Dependent events are influenced by previous events and their outcomes, while independent events are not affected by any previous events.

5. How can probability be used in real life situations?

Probability can be used in real life situations to make predictions, assess risk, and make decisions. It is often used in fields such as finance, insurance, and sports to make informed choices based on the likelihood of certain events occurring.

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