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Evan brought 77 bagels to school, 55 of which are blueberry.\newlineIf Evan randomly gives away 44 bagels to teachers, what is the probability that all of them are blueberry?\newlineWrite your answer as a decimal rounded to four decimal places.\newline____

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Q. Evan brought 77 bagels to school, 55 of which are blueberry.\newlineIf Evan randomly gives away 44 bagels to teachers, what is the probability that all of them are blueberry?\newlineWrite your answer as a decimal rounded to four decimal places.\newline____
  1. Calculate Probability of First Bagel: First, calculate the probability of picking a blueberry bagel on the first try.\newlineThere are 55 blueberry bagels out of 77 total bagels.\newlineProbability for the first bagel = Number of blueberry bagels / Total number of bagels = 57\frac{5}{7}.
  2. Calculate Probability of Second Bagel: Next, calculate the probability of picking a blueberry bagel on the second try, given that one blueberry bagel has already been given away.\newlineNow there are 44 blueberry bagels left and 66 total bagels.\newlineProbability for the second bagel = Number of remaining blueberry bagels / Total remaining bagels = 46\frac{4}{6}.
  3. Calculate Probability of Third Bagel: Then, calculate the probability of picking a blueberry bagel on the third try, given that two blueberry bagels have already been given away.\newlineNow there are 33 blueberry bagels left and 55 total bagels.\newlineProbability for the third bagel = Number of remaining blueberry bagels / Total remaining bagels = 35\frac{3}{5}.
  4. Calculate Probability of Fourth Bagel: Finally, calculate the probability of picking a blueberry bagel on the fourth try, given that three blueberry bagels have already been given away.\newlineNow there are 22 blueberry bagels left and 44 total bagels.\newlineProbability for the fourth bagel = Number of remaining blueberry bagels / Total remaining bagels = 24\frac{2}{4}.
  5. Multiply Individual Probabilities: Multiply all the individual probabilities together to get the overall probability of giving away four blueberry bagels in a row.\newlineOverall probability = (57)×(46)×(35)×(24)(\frac{5}{7}) \times (\frac{4}{6}) \times (\frac{3}{5}) \times (\frac{2}{4}).
  6. Calculate Overall Probability: Simplify and calculate the overall probability.\newlineOverall probability = (57)×(23)×(35)×(12)=(5×2×3×17×3×5×2)=30210(\frac{5}{7}) \times (\frac{2}{3}) \times (\frac{3}{5}) \times (\frac{1}{2}) = (\frac{5\times2\times3\times1}{7\times3\times5\times2}) = \frac{30}{210}.
  7. Reduce Fraction: Reduce the fraction 30210\frac{30}{210} to its simplest form.\newlineOverall probability = 30210=17\frac{30}{210} = \frac{1}{7}.

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