Question

30 serpentine outcrops occupied by populations of the Bay checkerspot occur very near one another. These outcrops are synchronized, experiencing very similar environmental conditions, predation risk, and disease risk in a given year and are similar in size. If each population has a 75% percent chance of extinction each year, what would you assume the odds are that any of these populations will be around in 2 years?

Answer 1

The statement in question proposes the idea of cumulative probability, through which we can conclude that there is a 6.25% chance of at least one of the outcrops being around in 2 years' time.

The cumulative probability property tells us that probabilities of an event occurring stack atop one another. Meaning that if we had a 10% chance to succeed at a task, it would not be correct to assume the probability of succeeding 5 times in a row will be the same.

The cumulative property tells us that the probability of the previous attempt affects the next one. So in the question, the odds of the crops surviving the first year are only 25%, which then gets multiplied by another 25 in order to calculate the odds that it will happen twice.

Given that the question is asking the odds for any of the populations to survive, we only use the probabilities of each isolated outcrop.

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