Question 1110816
<br>
The information about the numbers of puppies and kittens is not relevant to the question that is asked.<br>
You need to learn to recognize when information given in a problem can (should) be ignored.<br>
The ratio of cats to dogs is 5:4, so 5/9 of the 63 animals (35) are cats and 4/9 (28) are dogs.<br>
We are to determine what the most likely combination of cats and dogs is if we choose a total of 8 of the 63 animals.<br>
The probability of choosing (n) of the 35 cats and (8-n) of the 28 dogs is<br>
{{{(C(35,n)*C(28,8-n))/C(63,8)}}}<br>
We can calculate those probabilities for all possible values of n (0 to 8); however, it is reasonable to assume that the most likely combination, with the given numbers, is either 4 cats and 4 dogs, or maybe 5 cats and 3 dogs.  Actual calculations show<br>
P(4 cats, 4 dogs) = 0.2768
P(5 cats, 3 dogs) = 0.2746<br>
And the probabilities for the other combinations are indeed much lower than these.<br>
So the most likely combination is 4 cats and 4 dogs, with a probability of 0.2768.