Final answer:
The probability of landing on numbers 1, 3, and 4 on the dartboard is 1/16.
Step-by-step explanation:
In the given scenario, the probability of landing on a 2 is 1/4 and the probability of landing on a 5 is 3/8. We can determine the probability of landing on any other number by subtracting the probabilities of landing on 2 and 5 from 1.
Let's assume the probability of landing on numbers 1, 3, and 4 is x. Since the dartboard must contain numbers 1, 2, 3, 4, and 5, the sum of the probabilities of landing on these numbers should be 1. So, we have the equation:
x + 1/4 + x + 3/8 = 1
Combining like terms, we get:
2x + 7/8 = 1
Subtracting 7/8 from both sides, we have:
2x = 1 - 7/8
2x = 1/8
Dividing by 2, we get:
x = 1/16
Therefore, the probability of landing on numbers 1, 3, and 4 is 1/16.