Question

There were 25 horses performing at a dressage exhibition. Of these, 13 were of Westphalian breed and 2/3 of the remaining horses were of Andalusians breed.

If a horse is chosen at random, find the probability that it is neither Andalusian nor Westphalian.

Answer 1

The probability that a randomly chosen horse is neither Andalusian nor Westphalian is 4/25, as there are 4 horses of neither breed out of a total of 25 horses at the exhibition.

Step-by-step explanation:

The question is about calculating the probability of an event. There were 25 horses in a dressage exhibition with 13 Westphalian horses. To find out how many are Andalusian, we calculate 2/3 of the remaining horses. First, we subtract the number of Westphalian horses from the total, which leaves us with 25 - 13 = 12 horses. Then, we find 2/3 of these 12 horses, multiplied by 2/3 gives us 8 Andalusian horses.

We now know there are 13 Westphalian and 8 Andalusian horses, totaling 21 horses of these two breeds. Consequently, there are 25 - 21 = 4 horses that are of neither breed. Since there are 25 horses in total, the probability of choosing a horse that is neither Andalusian nor Westphalian is 4 out of 25, or 4/25. Therefore, if a horse is chosen at random, the probability that it is neither Andalusian nor Westphalian is 4/25.