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Joey volunteers at a children's hospital as an Art Director. He brought 88 T-shirts for the children to decorate this week. 55 of the T-shirts are a size small. If Joey was in a rush to get to the hospital, and he randomly grabbed 44 T-shirts to decorate, what is the probability that all of them are small? Write your answer as a decimal rounded to four decimal places.._________

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Q. Joey volunteers at a children's hospital as an Art Director. He brought 88 T-shirts for the children to decorate this week. 55 of the T-shirts are a size small. If Joey was in a rush to get to the hospital, and he randomly grabbed 44 T-shirts to decorate, what is the probability that all of them are small? Write your answer as a decimal rounded to four decimal places.._________
  1. Calculate Probability First T-shirt: First, calculate the probability of picking a small T-shirt on the first try.\newlineThere are 55 small T-shirts out of 88 total T-shirts.\newlineProbability for the first T-shirt = Number of small T-shirts / Total number of T-shirts = 58\frac{5}{8}.
  2. Calculate Probability Second T-shirt: Next, calculate the probability of picking a small T-shirt on the second try, given that the first T-shirt was small. Now there are 44 small T-shirts left and 77 T-shirts in total. Probability for the second T-shirt = 47\frac{4}{7}.
  3. Calculate Probability Third T-shirt: Then, calculate the probability of picking a small T-shirt on the third try, given that the first two T-shirts were small.\newlineNow there are 33 small T-shirts left and 66 T-shirts in total.\newlineProbability for the third T-shirt = 36\frac{3}{6}.
  4. Calculate Probability Fourth T-shirt: Finally, calculate the probability of picking a small T-shirt on the fourth try, given that the first three T-shirts were small.\newlineNow there are 22 small T-shirts left and 55 T-shirts in total.\newlineProbability for the fourth T-shirt = 25\frac{2}{5}.
  5. Multiply Probabilities: Multiply all the probabilities together to get the overall probability that all 44 T-shirts are small.\newlineOverall probability = (58)×(47)×(36)×(25)(\frac{5}{8}) \times (\frac{4}{7}) \times (\frac{3}{6}) \times (\frac{2}{5}).
  6. Perform Calculation: Now, perform the calculation.\newlineOverall probability = (58)×(47)×(12)×(25)=(5×4×1×28×7×2×5)=40560(\frac{5}{8}) \times (\frac{4}{7}) \times (\frac{1}{2}) \times (\frac{2}{5}) = (\frac{5 \times 4 \times 1 \times 2}{8 \times 7 \times 2 \times 5}) = \frac{40}{560}.
  7. Simplify Fraction: Simplify the fraction 40560\frac{40}{560} to its lowest terms.\newline40560=114.\frac{40}{560} = \frac{1}{14}.
  8. Convert to Decimal: Convert the fraction to a decimal and round to four decimal places. \newline114\frac{1}{14} as a decimal is approximately 0.07140.0714.

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