In a certain population of women, 40% have had breast cancer, 20% are smokers and 13% are smokers and have had breast cancer. if a woman is elected at random from the population, what is the probability that she had breast cancer, smokes or both?

40+20=60

this includes the sum of the women smoking and having cancer. i.e we have counted the women having cancer and smokes twice since they belong to both sets when one set is considered. Therefore we have to deduct one set of the common women from the previous sum.

60-13=47%

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents