text: +0
  
  # probability
  
  0
  100
  1
  
  A box contains 5 blue beads, 4 yellow beads and 3 purple beads. Three beads are taken from the bag, at random, without replacement.
  a) What is probability of picking, in order, a blue bead followed by a yellow bead followed by a purple bead?
  b) Work out the probability that all three beads will be the same colour.
  c) What is the probability that the three beads will not be the same colour.
  
  Apr 20, 2020
  
  #1
  +20767
  +2
  
  blue  =  5         yellow  =  4         purple  =  3          total  =  12
  
  a) blue      = 5/12
  
  yellow  =  4/11      (only 11 beads remain)
  
  purple  =  3/10      (only 10 beads remain)
  
  Multiplying these together:  5/12  x  4/11  x  3/10  =
  
  b)  to be three beads of the same color, they could:
  
  --   all be blue:          5/12  x  4/11  x  3/10     =  answer #1
  
  --   or all be yellow:  4/12  x  3/11  x  2/10     =  answer #2
  
  --   or all be purble:  3/12  x  2/11  x  1/10     =  answer #3
explanation: The provided text is a math problem involving probability. It contains a question with multiple parts (a, b, c) and a detailed answer for parts (a) and (b). The answer for part (c) is not provided.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: +0
  
  # probability
  
  0
  100
  1
  
  A box contains 5 blue beads, 4 yellow beads and 3 purple beads. Three beads are taken from the bag, at random, without replacement.
  a) What is probability of picking, in order, a blue bead followed by a yellow bead followed by a purple bead?
  b) Work out the probability that all three beads will be the same colour.
  c) What is the probability that the three beads will not be the same colour.
  
  Apr 20, 2020
  
  #1
  +20767
  +2
  
  blue  =  5         yellow  =  4         purple  =  3          total  =  12
  
  a) blue      = 5/12
  
  yellow  =  4/11      (only 11 beads remain)
  
  purple  =  3/10      (only 10 beads remain)
  
  Multiplying these together:  5/12  x  4/11  x  3/10  =
  
  b)  to be three beads of the same color, they could:
  
  --   all be blue:          5/12  x  4/11  x  3/10     =  answer #1
  
  --   or all be yellow:  4/12  x  3/11  x  2/10     =  answer #2
  
  --   or all be purble:  3/12  x  2/11  x  1/10     =  answer #3
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a math problem involving probability. It contains a question with multiple parts (a, b, c) and a detailed answer for parts (a) and (b). The answer for part (c) is not provided.
  
  Label: multiple-question-and-answer