I have 20% chance to have cavity gene. If I do have the gene, there is 51% chance that I will have at least one cavity over 1 year. If I don’t have the gene, there is 19% chance that I will have at least one cavity over 1 year. Given that I have a cavity in 6 months, what’s the probability that I have at least a cavity over 1 year?

Question

Sarabjeet · Accepted Answer

You can use the Bayes theorem to calculate the posterior probability of having the cavity gene.

P(gene | cavity 1) = P( cavity | gene) * P( gene) / P(cavity)
                         = 2/5 (rounding off all the probabilities)

Now, using the posterior probability, you can calculate the revised probability of having a cavity

P( cavity 2 | cavity 1) = P( cavity 2 | gene) * P( gene | cavity 1) + P( cavity 2 | no gene) * P( no gene | cavity 1)
                   = 8/25

ylchen · Answer

Anonymous · Answer

I also got 229/700

Anonymous · Answer

Last answer has a small error in the final calculation...the answer should be 2.29/7

Anonymous · Answer

33%?

Anonymous · Answer

The posterior probability of Gene seems to have been calculated wrong, I get 51/127!

Anonymous · Answer

3/7.

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