Addition rule for "OR"

Lessons

Lessons

1. Mutually Exclusive VS. Not Mutually Exclusive
   Consider the experiment of rolling a die.
   
   1. 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)
      
   2. 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)
      
   3. Supplementary info on mutually exclusive and addition rule.
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
   1. using the formula.
   2. using the Venn Diagram.
3. A card is drawn from a standard deck of 52 cards. Determine the probability that:
   1. a heart or a spade is drawn.
   2. a heart or a face card is drawn.
   3. an ace or a face card is drawn.
   4. an ace or a spade is drawn.
4. Use the following information to determine whether the events A, B are mutually exclusive.
   
   1. $P(A)=0.5$
      $P(B)=0.3$
      $P(A\;$or$\;B)=0.7$
   2. $P(A)=\frac{2}{3}$
      $P(B)=\frac{1}{5}$
      $P(A\;$or$\;B)=\frac{13}{15}$
   3. $P(A)=\frac{7}{12}$
      $P(B)=\frac{5}{13}$
      $P(A\;$and$\;B)=0$