Question

Dr. Al Maisari is a veterinarian who sees only dogs and cats.
In each appointment, he may or may not give the animal a vaccine.
The two-way frequency table summarizes Dr. Al Maisari's 50 appointments last week.

	Vaccine	no vaccine
dog	14	6
cat	11	19

Let dog be the event that a randomly chosen appointment (from the table) involved a dog.

Let vaccine be the event that a randomly chosen appointment (from the table) included a vaccine.

Find the following probabilities. Write your answers as decimals.

p(dog)=

p(vaccine dog)=

p(vaccine l dog)=

Answer 1

    dog : the event that a randomly chosen appointment (from the table) involved a dog                      
   vaccine : the event that a randomly chosen appointment (from the table) included a vaccine                      
   Total appointments = 50                      
                          
1)   To find P(dog)                      
   Total appointments for dog = 20                      
   Hence,                      
   P(dog) = 20/50                      
   P(dog) = 0.4                      
                          
                          
2)   To find P(dog)                      
   Total appointments for vaccine and dog = 14                      
   Hence,                      
   P(vaccine AND dog) = 14/50                      
   P(vaccine AND dog) = 0.28                      
                          
                          
3)   To find P(vaccine | dog)                      
   P(vaccine | dog)                      
   = P(vaccine AND dog) / P(dog)                      
   = 0.28/0.4                      
   = 0.7                      
   P(vaccine | dog) = 0.7                    

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