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Ken is a sandwich maker at a local deli. Last week, he tracked the number of peanut butter and jelly sandwiches ordered, noting the flavor of jelly and type of peanut butter requested. Creamy peanut butter Chunky peanut butter Strawberry jelly 4 3 Grape jelly 1 4 What is the probability that a randomly selected sandwich was made with grape jelly or was not made with creamy peanut butter? Simplify any fractions. ◻

Ken is a sandwich maker at a local deli. Last week, he tracked the number of peanut butter and jelly sandwiches ordered, noting the flavor of jelly and type of peanut butter requested.\newline\begin{tabular}{|l|c|c|}\newline\hline & Creamy peanut butter & Chunky peanut butter \\\newline\hline Strawberry jelly & 44 & 33 \\\newline\hline Grape jelly & 11 & 44 \\\newline\hline\newline\end{tabular}\newlineWhat is the probability that a randomly selected sandwich was made with grape jelly or was not made with creamy peanut butter?\newlineSimplify any fractions.\newline□ \square

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Q. Ken is a sandwich maker at a local deli. Last week, he tracked the number of peanut butter and jelly sandwiches ordered, noting the flavor of jelly and type of peanut butter requested.\newline\begin{tabular}{|l|c|c|}\newline\hline & Creamy peanut butter & Chunky peanut butter \\\newline\hline Strawberry jelly & 44 & 33 \\\newline\hline Grape jelly & 11 & 44 \\\newline\hline\newline\end{tabular}\newlineWhat is the probability that a randomly selected sandwich was made with grape jelly or was not made with creamy peanut butter?\newlineSimplify any fractions.\newline□ \square
  1. Count Total Sandwiches: First, let's count the total number of sandwiches made.\newlineTotal sandwiches = 44 (Strawberry jelly with Creamy peanut butter) + 33 (Strawberry jelly with Chunky peanut butter) + 11 (Grape jelly with Creamy peanut butter) + 44 (Grape jelly with Chunky peanut butter)\newlineTotal sandwiches = 4+3+1+4=124 + 3 + 1 + 4 = 12
  2. Find Grape Jelly Sandwiches: Now, let's find the number of sandwiches made with grape jelly.\newlineGrape jelly sandwiches = 11 (Grape jelly with Creamy peanut butter) + 44 (Grape jelly with Chunky peanut butter)\newlineGrape jelly sandwiches = 1+4=51 + 4 = 5
  3. Find Non-Creamy Peanut Butter Sandwiches: Next, let's find the number of sandwiches not made with creamy peanut butter.\newlineNon-creamy peanut butter sandwiches = 33 (Strawberry jelly with Chunky peanut butter) + 44 (Grape jelly with Chunky peanut butter)\newlineNon-creamy peanut butter sandwiches = 3+4=73 + 4 = 7
  4. Calculate Probability: Now, we need to find the probability of selecting a sandwich with grape jelly or not made with creamy peanut butter. However, we must be careful not to double-count the grape jelly sandwiches made with chunky peanut butter.
  5. Calculate Probability: The probability of selecting a sandwich with grape jelly or not made with creamy peanut butter is the sum of the probabilities of each individual event minus the probability of the overlap (sandwiches with grape jelly and chunky peanut butter).
    Probability = (Grape jelly sandwiches+Non-creamy peanut butter sandwiches−Overlap)/Total sandwiches(\text{Grape jelly sandwiches} + \text{Non-creamy peanut butter sandwiches} - \text{Overlap}) / \text{Total sandwiches}
    Overlap = 44 (Grape jelly with Chunky peanut butter)
    Probability = (5+7−4)/12(5 + 7 - 4) / 12
    Probability = (12−4)/12(12 - 4) / 12
    Probability = 8/128 / 12
  6. Simplify Fraction: Finally, we simplify the fraction.\newlineProbability = 812=23\frac{8}{12} = \frac{2}{3}

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