Question: A paleontologist in Patagonia discovers a set of 8 fossilized bones, 3 of which are from a Tyrannosaurus rex and 5 from a Triceratops. If she randomly selects 4 bones for detailed analysis, what is the probability that exactly 2 of the selected bones are from the Tyrannosaurus rex? - NBX Soluciones
A Fossil Discovery Sparking Strategic Curiosity—And Why Probability Matters Here
A Fossil Discovery Sparking Strategic Curiosity—And Why Probability Matters Here
In the quiet expanse of Patagonia, a paleontologist uncovers a remarkable assemblage of 8 fossilized bones: 3 from a fearsome Tyrannosaurus rex and 5 from a horned Triceratops. This find draws attention not just from museums and scientists—but from a growing audience fascinated by discovery, evolution, and the hidden stories buried deep in the earth. With the global interest in paleontology rising—fueled by documentaries, streaming science series, and public dig events—this real-world puzzle now finds its way into the digital space: what’s the chance of randomly selecting exactly 2 Tyrannosaurus rex bones when analyzing 4 from this set?
This question sits at the intersection of probability, chance, and scientific analysis—illustrating how mathematical reasoning helps us understand complex real-world processes. While DNA and fossil records often dominate the narrative, the math behind sampling offers fresh insight into how patterns emerge from random chance.
Understanding the Context
Why This Question Resonates in 2025
In recent months, discovery-based content has surged, especially around natural history and data-driven storytelling. This probability puzzle taps into a broader fascination: why do certain outcomes occur statistically? Whether users explore family roots, study ecology, or simply enjoy puzzle-based learning, such questions invite deeper engagement. The mix of geography, biology, and numbers appeals to the US audience’s curiosity about science, adventure, and real-world problem solving. Platforms prioritize content that educates while encouraging thoughtful reading—qualities this article delivers through clear, calm analysis.
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Solving the Probability: A Step-by-Step Overview
To determine the likelihood of selecting exactly 2 Tyrannosaurus rex bones from the 8 found (3 T. rex, 5 Triceratops), we rely on combinatorics—applied simply and clearly. Rather than overwhelming readers with formulas, the focus stays on meaningful context.
We want to pick 4 bones total, with exactly 2 from the T. rex group and 2 from the Triceratops group. The number of favorable combinations is calculated by:
- Choosing 2 out of 3 T. rex bones: given by the combination formula C(3,2) = 3
- Choosing 2 out of 5 Triceratops bones: C(5,2) = 10
- Multiply: 3 × 10 = 30 favorable combinations
The total number of ways to choose any 4 bones from 8 is C(8,4) = 70.
Thus, the probability is 30 out of 70, or 3/7—approximately 42.9%.
This breakdown shows how probability translates from abstract numbers into tangible understanding: the odds reflect both fragmentation in the sample and the natural distribution of the fossils.
