Name: _________________________________________________ Period: ___________ Date: ________________ CONDITIONAL PROBABILITY Assignment State which the following events are independent and which are dependent. 1. Drawing a card from a standard deck of playing card and flipping a penny 2. Drawing two disks from an jar without replacement of the first disk. 3. Winning the lottery and purchasing a new house 4. Driving on a high-speed highway and having an accident 5. Having a wide forehead and having a high IQ A box contains 8 red coins, 9 yellow coins, and 5 blue coins. Two consecutive draws are made from the bag without replacement of the first draw. Find the probability each of the following events. 6. Red first, red second 7. Red first, blue second 8. Red first, yellow second 9. Yellow first, blue second 10. Yellow first, yellow second 11. Yellow first, red second 12. Blue first, red second 13. Blue first, blue second 14. Blue first, yellow second. For one roll of a die, let π¨ be the event βevenβ and let π© the event β4 or 6β. Find each probability. 15. π·(π¨) 16. π·(π©) 17. π·(π¨ πππ π©) 18. π·(π© πππ π¨) 19. π·(π©|π¨) 20. π·(π¨|π©) π π 21. Given π·(π¨ πππ π©) = and π·(π¨) = , find π·(π©|π¨). π π 22. Given π·(π¨ πππ π©) = π. ππ and π·(π¨) = π. ππ, find π·(π©|π¨). π π 23. Given π·(π©|π¨) = π and π·(π¨) = π , find π·(π¨ πππ π©). Word Problem 24. A jar has 15 marbles, 3 of which are color red. If 2 are selected at random without replacing the first one, find the probability that both are color red. 25. In a country club, the probability that a member who play tennis is 75%. If 54% of the members play tennis and basketball, find the probability that the member who plays basketball, given that the member plays tennis. Copyright © Algebra2Coach.com 1 Name: _________________________________________________ Period: ___________ Date: ________________ CONDITIONAL PROBABILITY Assignment ANSWER State which the following events are independent and which are dependent. 1. Drawing a card from a standard deck of playing card and flipping a penny Independent 2. Drawing two disks from an jar without replacement of the first disk. Dependent 3. Winning the lottery and purchasing a new house Dependent 4. Driving on a high-speed highway and having an accident Dependent 5. Having a wide forehead and having a high IQ Independent A box contains 8 red coins, 9 yellow coins, and 5 blue coins. Two consecutive draws are made from the bag without replacement of the first draw. Find the probability each of the following events. 6. Red first, red second π π π·(π¨) = π·(πππ ) = = ππ ππ π π π π π π·(π¨ πππ π©) = π·(πππ πππ πππ ) = β = β = ππ ππ ππ π ππ π π·(π¨ πππ π©) ππ π ππ π π·(π©|π¨) = π·(πππ |πππ ) = = = β = π π·(π¨) ππ π π ππ π·(πππ |πππ ) = ππ. ππ% 7. Red first, blue second π·(π¨) = π·(πππ ) = π π = ππ ππ π π ππ β = ππ ππ πππ ππ π·(π¨ πππ π©) πππ ππ ππ π π·(π©|π¨) = π·(ππππ |πππ ) = = π = β = π·(π¨) πππ π ππ ππ π·(ππππ|πππ ) = ππ. ππ% π·(π¨ πππ π©) = π·(πππ πππ ππππ ) = 8. Red first, yellow second π·(π¨) = π·(πππ ) = π π = ππ ππ π π π π ππ β = β = ππ ππ ππ π ππ ππ π·(π¨ πππ π©) ππ ππ ππ π π·(π©|π¨) = π·(ππππππ |πππ ) = = π = β = π·(π¨) ππ π π ππ π·(ππππππ|πππ ) = ππ. ππ% π·(π¨ πππ π©) = π·(πππ πππ ππππππ ) = Copyright © Algebra2Coach.com 2 Name: _________________________________________________ Period: ___________ Date: ________________ CONDITIONAL PROBABILITY Assignment 9. Yellow first, blue second π·(π¨) = π·(ππππππ) = π ππ π π ππ β = ππ ππ πππ ππ π·(π¨ πππ π©) πππ ππ ππ π π·(π©|π¨) = π·(πππ |ππππππ) = = = β = π π·(π¨) πππ π ππ ππ π·(πππ |ππππππ) = ππ. ππ% π·(π¨ πππ π©) = π·(πππππππππ πππ ) = 10. Yellow first, yellow second π·(π¨) = π·(ππππππ) = π ππ π π ππ β = ππ ππ ππ ππ π·(π¨ πππ π©) ππ ππ ππ π π·(π©|π¨) = π·(πππ |ππππππ) = = π = β = ( ) π· π¨ ππ π ππ ππ π·(πππ |ππππππ) = ππ. ππ% π·(π¨ πππ π©) = π·(πππ πππ ππππππ) = 11. Yellow first, red second π·(π¨) = π·(ππππππ) = π ππ π π ππ β = ππ ππ ππ ππ π·(π¨ πππ π©) ππ ππ ππ π π·(π©|π¨) = π·(πππ |ππππππ) = = = β = π π·(π¨) ππ π ππ ππ π·(πππ |ππππππ) = ππ. ππ% π·(π¨ πππ π©) = π·(ππππππ πππ πππ ) = 12. Blue first, red second π·(π¨) = π·(ππππ ) = π ππ π π ππ β = ππ ππ πππ ππ π·(π¨ πππ π©) πππ ππ ππ π π·(π©|π¨) = π·(πππ |ππππ ) = = = β = ( ) π π· π¨ πππ π ππ ππ π·(πππ |ππππ ) = ππ. ππ% π·(π¨ πππ π©) = π·(ππππ πππ πππ ) = Copyright © Algebra2Coach.com 3 Name: _________________________________________________ Period: ___________ Date: ________________ CONDITIONAL PROBABILITY Assignment 13. Blue first, blue second π·(π¨) = π·(ππππ ) = π ππ π π ππ β = ππ ππ πππ ππ π·(π¨ πππ π©) πππ ππ ππ π π·(π©|π¨) = π·(ππππ |ππππ ) = = = β = ( ) π π· π¨ πππ π ππ ππ π·(ππππ |ππππ ) = ππ. ππ% π·(π¨ πππ π©) = π·(ππππ πππ ππππ ) = 14. Blue first, yellow second. π·(π¨) = π·(ππππ ) = π ππ π π π π ππ β = β = ππ ππ ππ π πππ ππ π·(π¨ πππ π©) πππ ππ ππ π π·(π©|π¨) = π·(ππππππ|ππππ ) = = = β = ( ) π π· π¨ πππ π π ππ π·(ππππππ|ππππ ) = ππ. ππ% π·(π¨ πππ π©) = π·(ππππ πππ ππππππ) = For one roll of a die, let π¨ be the event βevenβ and let π© the event β4 or 6β. Find each probability. 15. π·(π¨) π π π·(π¨) = = π·(π¨) = π π 16. π·(π©) π·(π©) = π π π π + = = π·(π©) = π π π π 17. π·(π¨ πππ π©) π·(π¨ πππ π©) = 18. π·(π© πππ π¨) π·(π© πππ π¨) = 19. π·(π©|π¨) 20. π·(π¨|π©) π π π β = π·(π¨ πππ π©) = π π π π π π β = π·(π© πππ π¨) = π π π π π·(π¨ πππ π©) π π π π π·(π©|π¨ ) = = π = β = π·(π©|π¨) = π·(π¨) π π π π π π·(π© πππ π¨) π π π π π·(π¨| π©) = = π = β = π·(π¨|π©) = π·(π©) π π π π Copyright © Algebra2Coach.com 4 Name: _________________________________________________ Period: ___________ Date: ________________ CONDITIONAL PROBABILITY Assignment π π 21. Given π·(π¨ πππ π©) = and π·(π¨) = , find π·(π©|π¨). π π π π·(π¨ πππ π©) π π π π π·(π©|π¨) = = 1 = β = π·(π©|π¨) = π·(π¨) π π π 2 22. Given π·(π¨ πππ π©) = π. ππ and π·(π¨) = π. ππ, find π·(π©|π¨). π·(π¨ πππ π©) π. ππ π·(π©|π¨) = = = π. ππππ = π·(π©|π¨) β ππ. ππ% π·(π¨) π. ππ π π π π 23. Given π·(π©|π¨) = and π·(π¨) = , find π·(π¨ πππ π©). π π π π·(π¨ πππ π©) = π·(π©|π¨) β π·(π¨) = ( ) ( ) = = π·(π¨ πππ π©) β ππ. ππ% π π π Word Problem 24. A jar has 15 marbles, 3 of which are color red. If 2 are selected at random without replacing the first one, find the probability that both are color red. π π π·(π¨) = π·(πππ ) = = ππ π π·(π¨ πππ π©) = π·(πππ πππ πππ ) = π π π π π β = β = π ππ π π ππ π π·(π¨ πππ π©) ππ π π π π·(π©|π¨) = π·(πππ |πππ ) = = π = β = π·(π¨) ππ π π π π·(πππ |πππ ) β ππ. ππ% 25. In a country club, the probability that a member who play tennis is 75%. If 54% of the members play tennis and basketball, find the probability that the member who plays basketball, given that the member plays tennis. π·(π¨) = π·(ππππππ) = π. ππ π·(π¨ πππ π©) = π·(ππππππ πππ ππππππππππ) = π. ππ π·(π©|π¨) = π·(ππππππππππ|ππππππ ) = π·(π¨ πππ π©) π. ππ = = π. ππ π·(π¨) π. ππ π·(ππππππππππ|ππππππ ) = ππ% Copyright © Algebra2Coach.com 5
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