Current learning objective: The Addition Rule Question 4 Score: 0 of 1 point In a box of assorted cookies, \( 39 \% \) contain chocolate and \( 14 \% \) contain nuts, In the box, \( 6 \% \) contain both chocolate and nuts, Sean is allergic to both chocolate and nuts. Find the probability that a cookie contains chocolate or nuts (he can't eat it). Enter your answer Find the probability that a cookie does not contain chocolate or nuts (he can eat it). Enter your answer

To find the probability that a cookie contains chocolate or nuts, we can use the Addition Rule for probabilities. The formula is: \[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \] In this case: - \( P(\text{chocolate}) = 39\% = 0.39 \) - \( P(\text{nuts}) = 14\% = 0.14 \) - \( P(\text{chocolate and nuts}) = 6\% = 0.06 \) So, \[ P(\text{chocolate or nuts}) = 0.39 + 0.14 - 0.06 = 0.47 \] This means there’s a \( 47\% \) chance that a cookie contains chocolate or nuts, making it unsafe for Sean to eat. To find the probability that a cookie does not contain chocolate or nuts, we subtract the probability of chocolate or nuts from 1: \[ P(\text{not (chocolate or nuts)}) = 1 - P(\text{chocolate or nuts}) = 1 - 0.47 = 0.53 \] Thus, there's a \( 53\% \) chance that a cookie does not contain chocolate or nuts, meaning it's safe for Sean to eat! In conclusion: 1. \( P(\text{chocolate or nuts}) = 0.47 \) 2. \( P(\text{not (chocolate or nuts)}) = 0.53 \)