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Conditional Probability – A C o lo r Sequence Example

Conditional Probability – A C o lo r Sequence Example. Compute Pr{ blue shows 1 st | blue shows 4 th }. Pr{ blue shows 1 st | blue shows 4 th } Identify Prior Event “Blue Shows 4 th “. Pr{ blue shows 1 st | blue shows 4 th }; Compute Prior Probability Pr{ Blue Shows 4 th } =

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Conditional Probability – A C o lo r Sequence Example

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  1. Conditional Probability – A Color Sequence Example

  2. Compute Pr{ blue shows 1st | blue shows 4th }

  3. Pr{ blue shows 1st | blue shows 4th} Identify Prior Event “Blue Shows 4th “

  4. Pr{ blue shows 1st | blue shows 4th}; Compute Prior Probability Pr{ Blue Shows 4th } = Pr{ exactly one of BBBB, BGGB, RYYB shows } = Pr{BBBB} + Pr{BGGB} + Pr{RYYB} = .10+.25+.15 = .50

  5. Pr{ blue shows 1st | blue shows 4th} Identify Joint Probability “Blue Shows 1st and 4th “

  6. Pr{ blue shows 1st | blue shows 4th} Compute Joint Probability Pr{ Blue Shows 1st and 4th } = Pr{ exactly one of BBBB, BGGB shows } = Pr{BBBB} + Pr{BGGB} = .10+.25 = .35

  7. Conditional Probability = Joint Probability / Prior Probability So, Pr{ Blue Shows 1st | Blue Shows 4th } = Pr{ Blue Shows 1st and 4th }/Pr{Blue Shows 4th } = .35/ .50= .70

  8. Compute Pr{ green shows 2nd or 3rd | yellow shows }

  9. Pr{ green shows 2nd or 3rd | yellow shows }; Identify Prior Event “Yellow Shows”

  10. Pr{ green shows 2nd or 3rd | yellow shows } Compute Prior Probability Pr{ Yellow Shows } = Pr{ exactly one of YYYY, BYRG, RYYB shows } = Pr{YYYY}+ Pr{BYRG}+ Pr{RYYB} = .30+.15+.15 = .60

  11. Identify Joint Event “Green Shows 2nd or 3rd and Yellow Shows” No sequences meet this requirement, so Pr{“Green Shows 2nd or 3rd and Yellow Shows”} = 0

  12. Conditional Probability = Joint Probability / Prior Probability So Pr{ Green Shows 2nd or 3rd | Yellow shows } = Pr{ Green Shows 2nd or 3rd and Yellow shows }/ Pr{Yellow shows } = 0 / .60= 0

  13. Compute Pr{ yellow shows | red shows }

  14. Pr{ yellow shows | red shows } Identify Prior Event “Red Shows”

  15. Compute Prior Probability Pr{ Red Shows } = Pr{ exactly one of RGGR, BYRG, RYYB shows } = Pr{RGGR} + Pr{BYRG} + Pr{RYYB } = .05+.15+.15 = .35

  16. Pr{ yellow shows | red shows } Identify Joint Probability “ Yellow and Red Show “

  17. Compute Joint Probability Pr{ Yellow and Red Show } = Pr{ exactly one of BYRG, RYYB shows } = Pr{BYRG}+ Pr{RYYB } = .15 + .15 = .30

  18. Conditional Probability = Joint Probability / Prior Probability So Pr{ Yellow Shows | Red Shows } = Pr{ Yellow and Red Shows }/Pr{Red Shows } = .30/.35 = 6/7 = .8571

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