A mammalogist observes a group of 20 dolphins and records that 12 are males and 8 are females. If she randomly selects 4 dolphins without replacement, what is the probability that exactly 2 are male? - Treasure Valley Movers
What Dolphin Demographics Reveal About Probability—and Insight into Wildlife Science
What Dolphin Demographics Reveal About Probability—and Insight into Wildlife Science
When tracking animal behavior in natural habitats, scientists often rely on precise data to understand patterns—like the distribution of male and female individuals in a group. A recent study observed 20 dolphins, noting 12 males and 8 females. From this baseline, researchers asked a core statistical question: What’s the chance that, if selecting four dolphins at random without replacement, exactly two will be male? This seemingly simple query reflects deeper interests in population dynamics, probabilistic thinking, and how science observes the natural world with measurable rigor.
Why is this kind of analysis gaining renewed attention in the US landscape? It mirrors a growing public fascination with wildlife behavior, shaping trends in documentaries, citizen science apps, and educational content. Understanding such probabilities deepens curiosity about how animal groups function—insights valuable not just to biologists, but to anyone interested in patterns behind wildlife observations.
Understanding the Context
Now, let’s break down what happens when four dolphins are chosen from this group. The task follows a standard combinatorics approach: sampling without replacement from 20 total dolphins—12 males and 8 females—with the goal of computing the exact probability that exactly two of the four selected are male.
Step-by-Step: Breaking the Probability
The scenario uses combinatorial counting. The total number of ways to choose 4 dolphins from 20 is given by the combination formula:
C(20, 4) = 4845.
To find favorable outcomes—where exactly two are male and two female—we compute:
Key Insights
- Ways to choose 2 males from 12: C(12, 2) = 66
- Ways to choose 2 females from 8: C(8, 2) = 28
Multiplying these gives favorable combinations:
66 × 28 = 1848
Thus, the probability is:
