Question

If four dogs are picked up from the Veterinarian and they are returned to their owners at random, what is the probability that at least one owner receives the wrong dog? Round your answer to two decimal places.

Answer 1

is 1 outta 4

Answer 2

or .25

Answer 3

again "at least one" means you want to compute the probability that none receive the correct dog, and subtract that number from one

Answer 4

at least one means one or two or three or four. easier to compute none

Answer 5

so lets go slow. we want to compute the probability that each owner gets the right dog. we have 4 dogs and the first owner gets the right one so that probability is

\[\frac{1}{4}\]
now we have 3 dogs to choose from and the probability that next owner gets right dog is
\[\frac{1}{3}\] and for the next one
\[\frac{1}{2}\]

so the probability that each owner gets the right dog is very small, namely
\[\frac{1}{4}\times \frac{1}{3}\times \frac{1}{2}=\frac{1}{24}\]

Answer 6

therefore the probability that AT LEAST ONE owner gets the wrong dog is
\[1-\frac{1}{24}=\frac{23}{24}\]

Answer 7

i love how u explain it i get it right after thank you!

Answer 8

sorry first line i wrote above says

again "at least one" means you want to compute the probability that none receive the correct dog, and subtract that number from one

what i meant to say was AT LEAST ONE GETS THE WRONG DOG MEANS YOU WANT TO COMPUTE THE PROBABILITY THAT THEY ALL GET THE RIGHT DOG
and then subtract from one. the rest is correct

Answer 9

yw

Answer 10

ohh okay