Final answer:
Each child will receive 7 cookies with a remainder of 1 cookie when 15 chocolate chip cookies are divided between 2 children. The probability that a cookie contains chocolate or nuts is 40%, and the probability that it does not contain these allergens is 60%.
Step-by-step explanation:
If 15 chocolate chip cookies are to be evenly divided between 2 children, each child would get 7 cookies with a remainder of 1 cookie because 15 divided by 2 equals 7 with a remainder of 1. This mathematical operation is known as division, which involves dividing a total or a number (in this case, 15 cookies) by the number of groups or recipients (2 children).
Considering the provided information regarding probabilities, if a student has an allergy and needs to find the probability that a cookie contains chocolate or nuts (which the student cannot eat), we use the formula P(C OR N) = P(C) + P(N) - P(C AND N), where C is the event that the cookie contains chocolate and N is the event that the cookie contains nuts. Given that 36% contain chocolate (P(C) = 0.36), 12% contain nuts (P(N) = 0.12), and 8% contain both (P(C AND N) = 0.08), the calculation yields P(C OR N) = 0.36 + 0.12 - 0.08 = 0.40, which means there's a 40% chance that a cookie contains either chocolate or nuts.
To find the probability that a cookie does not contain chocolate or nuts, we calculate P(NEITHER chocolate NOR nuts) = 1 - P(C OR N) = 1 - 0.40 = 0.60, which gives us a 60% chance that a cookie can be eaten by someone allergic to both chocolate and nuts.