Calculating the Probability of Horse A winning:
The probability of Horse A winning the race is given as 1/6.

Calculating the Probability of Horse B winning:
The probability of Horse B winning the race is given as 1/4.

Calculating the Probability of None of them winning:
To calculate the probability that none of them will win, we need to find the probability of both Horse A and Horse B not winning the race.
The probability of Horse A not winning the race is 1 - 1/6 = 5/6.
Similarly, the probability of Horse B not winning the race is 1 - 1/4 = 3/4.

Since the outcome of Horse A winning and Horse B winning are independent events, we can multiply their probabilities together to find the probability of both events not occurring.

Calculating the Probability of None of them winning:
Probability of none of them winning = Probability of Horse A not winning * Probability of Horse B not winning
= (5/6) * (3/4)
= 15/24
= 5/8

Therefore, the probability that none of them will win the race is 5/8 or 0.625.

Explanation:
To calculate the probability of none of them winning the race, we need to find the individual probabilities of Horse A and Horse B not winning the race. The probability of an event occurring is equal to one minus the probability of the event not occurring. So, the probability of Horse A not winning the race is 1 - 1/6, which is equal to 5/6. Similarly, the probability of Horse B not winning the race is 1 - 1/4, which is equal to 3/4. Since the outcome of Horse A winning and Horse B winning are independent events, we can multiply their probabilities together to find the probability of both events not occurring. Therefore, the probability of none of them winning the race is (5/6) * (3/4) = 15/24 = 5/8 or 0.625.