Probability of independent events

Lessons

• Introduction
  Differences between independent events and dependent events
  a)

  Differences between independent events and dependent events
  
  
  b)

  Addition and multiplication rules for probability
  
  
  c)

  Experimental probability VS. Theoretical probability
  
  

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• 1.
  A spinner divided in 4 equal sections is spun. Each section of the spinner is labeled 1, 2, 3, and 4. A marble is also drawn from a bag containing 5 marbles: one green, one red, one blue, one black, and one white. Find the probability of:
  a)

  Landing on section 2 and getting the green marble.
  
  
  b)

  Not landing on section 3 and not getting the black marble.
  
  
  c)

  Landing on section 1 or 4 and getting the red or blue marble.
  
  
  d)

  Landing on any section and getting the white marble.
  
  

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• 2.
  A coin is flipped, a standard six-sided die is rolled; and a spinner with 4 equal sections in different colours is spun (red, green, blue, yellow). What is the probability of:
  a)

  Getting the head, and landing on the yellow section?
  
  
  b)

  Getting the tail, a 6 and landing on the red section?
  
  
  c)

  Getting the tail, a 2 and not landing on the blue section?
  
  
  d)

  Not getting the tail; not getting a 3; and not landing on the blue section?
  
  
  e)

  Not getting the head; not getting a 5; and not landing on the green section?
  
  

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• 3.
  A toy vending machine sells 5 types of toys including dolls, cars, bouncy balls, stickers, and trains. The vending machine has the same number of each type of toys, and sells the toys randomly. Don uses a five-region spinner to simulate the situation. The results are shown in the tall chart below:

  Doll	Car	Bouncy Ball	Sticker	Train
  ||||	||||	|||	||	||

  a)

  Find the experimental probability of P(doll).
  
  
  b)

  Find the theoretical probability of P(doll).
  
  
  c)

  Compare the experimental probability and theoretical probability of getting a doll. How to improve the accuracy of the experimental probability?
  
  
  d)

  Calculate the theoretical probability of getting a train 2 times in a row?
  
  

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