Addition rule for "OR"

Lessons

• Introduction

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• 1.
  Mutually Exclusive VS. Not Mutually Exclusive
  Consider the experiment of rolling a die.
  
  a)

  Event A: an even number is thrown
  Event B: an odd number is thrown
  i) List the outcomes for:
  $\cdot$ event A
  $\cdot$ event B
  $\cdot$ event A or B
  $\cdot$ event A and B
  ii) Mark the outcomes on the Venn Diagram. Are events A, B mutually exclusive?
  iii) Determine the following probabilities:
  $\cdot$ P(A)
  $\cdot$ P(B)
  $\cdot$ P(A or B)
  $\cdot$ P(A and B)
  
  
  
  b)

  Event A: an even number is thrown
  Event B: a multiple of three is thrown
  i) List the outcomes for:
  $\cdot$ event A
  $\cdot$ event B
  $\cdot$ event A or B
  $\cdot$ event A and B
  ii) Mark the outcomes on the Venn Diagram. Are events A, B mutually exclusive?
  iii) Determine the following probabilities:
  $\cdot$ P(A)
  $\cdot$ P(B)
  $\cdot$ P(A or B)
  $\cdot$ P(A and B)
  
  
  
  c)

  Supplementary info on mutually exclusive and addition rule.
  
  

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• 2.
  There are 20 students in a class. 9 students like pizza and 7 students like pasta. Of these students, 3 students like both. Determine the probability that a randomly selected student in the class like pizza or pasta
  a)

  using the formula.
  
  
  b)

  using the Venn Diagram.
  
  

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• 3.
  A card is drawn from a standard deck of 52 cards. Determine the probability that:
  a)

  a heart or a spade is drawn.
  
  
  b)

  a heart or a face card is drawn.
  
  
  c)

  an ace or a face card is drawn.
  
  
  d)

  an ace or a spade is drawn.
  
  

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• 4.
  Use the following information to determine whether the events A, B are mutually exclusive.
  
  a)

  $P(A)=0.5$

  $P(B)=0.3$

  $P(A\;$or$\;B)=0.7$
  
  
  b)

  $P(A)=\frac{2}{3}$

  $P(B)=\frac{1}{5}$

  $P(A\;$or$\;B)=\frac{13}{15}$
  
  
  c)

  $P(A)=\frac{7}{12}$

  $P(B)=\frac{5}{13}$

  $P(A\;$and$\;B)=0$
  
  

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