Mathematics

Question

n the waiting room of a vet's office, there are 4 cats, 5 dogs, 1 lizard, and 1 hamster. A represents the event that a randomly selected animal in this waiting room is a dog. What is the probability of the complement of event A? Enter your answer as a fraction, in simplified form, in the box

2 Answer

  • the answer 5/11. you add all those numbers up (thats the denominator) and put the 5 representing a dog on top of the fraction
  • Answer:

    The probability is:

                   [tex]\dfrac{6}{11}[/tex]

    Step-by-step explanation:

    There are 4 cats, 5 dogs, 1 lizard, and 1 hamster.

    A represents the event that a randomly selected animal in this waiting room is a dog.

    This means that the probability of A is the ratio of number of dogs to the total number of animals.

    i.e.

    [tex]P(A)=\dfrac{5}{11}[/tex]

    ( Since the total number of animals are: 11

    and the total number of dogs=5 )

    Also, the probability of complement of A is given by:

    [tex]P(A^c)=1-P(A)[/tex]

    Hence,

    [tex]P(A^c)=1-\dfrac{5}{11}\\\\\\P(A^c)=\dfrac{11-5}{11}\\\\\\P(A^c)=\dfrac{6}{11}[/tex]

                Hence, the answer is:

                        [tex]P(A^c)=\dfrac{6}{11}[/tex]

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