Final answer:
The probability of choosing a humbug from the jar is calculated using the number of humbugs, which is 2x + 6, and the total number of sweets, which is 3x + 9. The probability expression is P(humbug) = (2x + 6) / (3x + 9), which simplifies to (2x/3 + 2) / (x + 3).
Step-by-step explanation:
The subject of the question is probability, a concept within the field of mathematics. The problem presents a situation with a jar of sweets containing 3 types of sweets: Eclairs, humbugs, and mints. There are 3 Eclairs, 2x + 6 humbugs, and x mints. To find the probability of choosing a humbug at random, we must first determine the total number of sweets in the jar.
- Number of Eclairs = 3
- Number of humbugs = 2x + 6
- Number of mints = x
The total number of sweets is the sum of Eclairs, humbugs, and mints: T = 3 + (2x + 6) + x = 3x + 9.
The probability of choosing a humbug is given by the number of humbugs divided by the total number of sweets: P(humbug) = (2x + 6) / (3x + 9). To simplify, you can divide the numerator and the denominator by 3, resulting in: P(humbug) = (2x/3 + 2) / (x + 3). Without specific values for x, we can only express the probability in terms of x.