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20242024 G-Survey of Mathematics (MATH−1130-1130−1020-1020)\newlineArlene Hood 0303/2828/2424 66:5151 PM\newline(?)\newlineAll Book\newlineork: \newline1111.55HW -\newlineHW Score: \newline5050.7979\%,1010.6767 of\newlineility with the\newlineQuestion 1414, 1111.55.1717\newline2121 points\newlinePoints: 00 of 11\newlineSave\newlinelist \newlinequad K\newlineIf you are dealt 33 cards from a shuffled deck of 5252 cards, find the probability that all 33 cards are picture cards.\newlineThe probability is \newline□\square.\newline(Round to six decimal places as needed.)

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Q. 20242024 G-Survey of Mathematics (MATH−1130-1130−1020-1020)\newlineArlene Hood 0303/2828/2424 66:5151 PM\newline(?)\newlineAll Book\newlineork: \newline1111.55HW -\newlineHW Score: \newline5050.7979\%,1010.6767 of\newlineility with the\newlineQuestion 1414, 1111.55.1717\newline2121 points\newlinePoints: 00 of 11\newlineSave\newlinelist \newlinequad K\newlineIf you are dealt 33 cards from a shuffled deck of 5252 cards, find the probability that all 33 cards are picture cards.\newlineThe probability is \newline□\square.\newline(Round to six decimal places as needed.)
  1. Determine total picture cards: Determine the total number of picture cards in a deck.\newlineIn a standard deck of 5252 cards, there are 1212 picture cards (44 Jacks, 44 Queens, and 44 Kings).
  2. Calculate first card probability: Calculate the probability of drawing the first picture card.\newlineThe probability of drawing a picture card on the first draw is the number of picture cards divided by the total number of cards in the deck.\newlineProbability = Number of picture cards / Total number of cards = 1252\frac{12}{52}
  3. Calculate second card probability: Calculate the probability of drawing the second picture card after the first has been drawn.\newlineNow there are 1111 picture cards left and 5151 cards in total.\newlineProbability = Number of remaining picture cards / Total remaining cards = 1151\frac{11}{51}
  4. Calculate third card probability: Calculate the probability of drawing the third picture card after two have been drawn.\newlineNow there are 1010 picture cards left and 5050 cards in total.\newlineProbability = Number of remaining picture cards / Total remaining cards = 1050\frac{10}{50}
  5. Multiply probabilities: Multiply the probabilities from each draw to find the overall probability of drawing 33 picture cards in a row.\newlineOverall probability = (1252)×(1151)×(1050)(\frac{12}{52}) \times (\frac{11}{51}) \times (\frac{10}{50})
  6. Perform calculation: Perform the calculation.\newlineOverall probability = (1252)×(1151)×(1050)=12×11×1052×51×50(\frac{12}{52}) \times (\frac{11}{51}) \times (\frac{10}{50}) = \frac{12 \times 11 \times 10}{52 \times 51 \times 50}\newlineOverall probability = 1320132600\frac{1320}{132600}\newlineOverall probability = 0.0099502487562189050.009950248756218905
  7. Round result: Round the result to six decimal places as instructed.\newlineThe probability rounded to six decimal places is approximately 0.0099500.009950.

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