There are ten ways to have one error (0.99^{9} × 0.01^{1} × 10) and 45 ways to have two errors (0.99^{8} × 0.01^{2} × 45). These add up to 9.6%.

2 thoughts on “Puzzle #160 Solution: Oops!”

Lynne Mugford

Could this be another oops? Shouldn’t the percentage be greater than 10 %? Since the probability of making an error is 1 %, the probability of making exactly one error in ten weeks should be 10 %?

Thanks,

Lynne

Gene WirchenkoPost author

Nope. Would the probability of making exactly one error in 100 weeks be 100%? Would the probability of making exactly one error in 200 weeks be 200%? The probabilities do not add in this case. Look up the birthday problem: how many people (selected randomly) are needed to have at least 50% probability that at least two of them will share birthdays? The answer is lower than you almost certainly think (if you have not seen this problem before).

Lynne MugfordCould this be another oops? Shouldn’t the percentage be greater than 10 %? Since the probability of making an error is 1 %, the probability of making exactly one error in ten weeks should be 10 %?

Thanks,

Lynne

Gene WirchenkoPost authorNope. Would the probability of making exactly one error in 100 weeks be 100%? Would the probability of making exactly one error in 200 weeks be 200%? The probabilities do not add in this case. Look up the birthday problem: how many people (selected randomly) are needed to have at least 50% probability that at least two of them will share birthdays? The answer is lower than you almost certainly think (if you have not seen this problem before).