Math shows a failed recall

Re “715,833 names on effort to recall Gascon,” July 10

At least 566,857 valid signatures are needed to force a recall election of Los Angeles County Dist. Atty. George Gascón. A total of 715,833 signatures were submitted.

Election workers randomly sampled 35,793 of these signatures and found that 27,983 of them were valid, which was not enough to certify an election. They will now make a full check of all the signatures to see if at least 566,857 are valid.

However, if at least 566,857 of the signatures collected were valid, then the probability that a random sample of 35,793 of the 715,833 would have as few as 27,983 valid signatures is 0.000000836. That is, the probability, obtained by using the distribution function of a hypergeometric random variable, is less than 1 in a million.

Conclusion: If the sample of signatures checked for validity was really a random sample, then there is no way that a recall election will be held.

Sheldon Ross

Santa Monica The writer is a USC engineering professor who specializes in probability theory.