A chemical engineer is testing 12 new sustainable solvents: 5 are water-based, 4 are bio-based, and 3 are ionic. If 6 solvents are selected at random, what is the probability that at least one solvent from each type is included? - Treasure Valley Movers
A chemical engineer is testing 12 new sustainable solvents: 5 are water-based, 4 are bio-based, and 3 are ionic. If 6 solvents are selected at random, what is the probability that at least one solvent from each type is included?
A chemical engineer is testing 12 new sustainable solvents: 5 are water-based, 4 are bio-based, and 3 are ionic. If 6 solvents are selected at random, what is the probability that at least one solvent from each type is included?
As industries shift toward greener alternatives, innovations in sustainable chemistry are drawing growing attention in the U.S. Efforts to replace traditional solvents—often toxic and environmentally harmful—with eco-friendly options are accelerating. A recent development involves a chemical engineer evaluating 12 new sustainable solvent prototypes: 5 water-based, 4 bio-based, and 3 ionic. If six solvents are selected at random, what is the probability that each type is represented? This question reflects both scientific progress and rising demand for safer industrial chemicals.
Understanding the Scope of Solvent Innovation
The field of green solvents is gaining momentum across manufacturing, pharmaceuticals, and environmental science. With increasing pressure to reduce carbon footprints and comply with stricter safety regulations, chemical engineers are testing novel formulas that balance performance and sustainability. The current cluster of 12 solvents—diverse in composition and potential use—represents a critical data point in this evolution. When selecting a random subset of six, the chance of capturing all three solvent types offers valuable insight into compatibility and representation in emerging markets.
Understanding the Context
What Does It Mean to Include a Solvent from Each Type?
Each solvent class serves a unique purpose: water-based systems offer low toxicity and easy disposal; bio-based solvents reduce reliance on fossil feedstocks; ionic liquids provide exceptional stability and recyclability. Meeting a representative mix helps assess versatility, risk mitigation, and product compatibility in real-world applications—key factors for industries adopting sustainable practices.
Calculating the Probability: A Step-by-Step Breakdown
To determine the probability that at least one solvent from each type appears in a random selection of 6 from the 12, begin with
