E. Chapter 3 HW-Probability Topics Current learning objective: The Addition Rule Question 28 Practice similar questions Score: 0 of 2 points In a box of assorted cookies, \( 32 \% \) contain chocolate and \( 15 \% \) contain nuts. In the box, \( 12 \% \) 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 \begin{tabular}{l}\( \sqrt{x} \) \\ \hline\end{tabular}

To find the probability that a cookie contains chocolate or nuts, we can use the Addition Rule for probabilities: \[ P(\text{Chocolate or Nuts}) = P(\text{Chocolate}) + P(\text{Nuts}) - P(\text{Chocolate and Nuts}) \] Substituting the values we have: \[ P(\text{Chocolate or Nuts}) = 0.32 + 0.15 - 0.12 = 0.35 \] So, the probability that a cookie contains chocolate or nuts is \( 0.35 \) or \( 35\% \). Now, to find the probability that a cookie does not contain chocolate or nuts, we subtract the probability of getting chocolate or nuts from 1: \[ P(\text{Not Chocolate and Not Nuts}) = 1 - P(\text{Chocolate or Nuts}) = 1 - 0.35 = 0.65 \] Thus, the probability that a cookie does not contain chocolate or nuts (which Sean can eat) is \( 0.65 \) or \( 65\% \).