Final answer:
The probability that a cookie contains chocolate or nuts is 40%, while the probability that a cookie does not contain either is 60%.
Step-by-step explanation:
To solve this problem, we need to use the principles of probability. The probability that a cookie contains either chocolate or nuts can be expressed as the sum of the individual probabilities minus the probability of both occurring at the same time. Given that 36% of the cookies contain chocolate and 12% contain nuts, with 8% containing both chocolate and nuts, we can add the two probabilities and subtract the overlap.
P(Chocolate or Nuts) = P(Chocolate) + P(Nuts) - P(Both)
P(Chocolate or Nuts) = 36% + 12% - 8% = 40%
Therefore, the probability that a cookie contains chocolate or nuts is 40%, and Sean cannot eat these. To find the probability of a cookie that he can eat, we subtract from 100% which represents the whole set of cookies.
P(Does not contain Chocolate or Nuts) = 100% - P(Chocolate or Nuts)
P(Does not contain Chocolate or Nuts) = 100% - 40% = 60%
The probability that a cookie does not contain chocolate or nuts, and thus Sean can eat, is 60%.