Respuesta :
The probability helps us to know the chances of an event occurring. The theoretical probability that they have three dogs or three cats is 0.25.
What is Probability?
The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that the pet can either be a dog or a cat, therefore,
The probability that all the three pets are dogs is:
[tex]\rm P(X= 3\ dogs) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]
The probability that all the three pets are cats is:
[tex]\rm P(X= 3\ Cats) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]
Now, we need to calculate the probability that all three pets are either dogs or cats, therefore, the probability can be written as,
[tex]\rm P(3\ Dogs\ or\ 3\ Cats) = P(X = 3\ dogs) + P(X = 3\ cats)[/tex]
[tex]= \dfrac{1}{8}+\dfrac{1}{8}\\\\=\dfrac{2}{8}\\\\ = \dfrac{1}{4} = 0.25[/tex]
Hence, the theoretical probability that they have three dogs or three cats is 0.25.
Learn more about Probability:
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