a group of biologists study a population of squirrels in order to estimate the probability that a squirrels food storage will survive through the winter. based on data gathered across several years, the biologists report that the probability a squirrel will successfully store its food is equal to 0.82. from this information, along with what you know about probability, which one of the following statements is correct?

because probabilities cannot be greater than 1 or negative, 0.82 is a legitimate probability.

because probabilities can only be 0.5 or smaller, 0.82 is not a legitimate probability.

because the number 0.82 was based on past data, it should be called a prediction instead of being called a probability.

because a probability of 0.82 is equivalent to a percentage of 82%, and because 82 is larger than 1, it is impossible for a probability to equal 0.82.

because the value 0.82 was calculated from a sample, it is a statistic and not a true probability.

Question

a group of biologists study a population of squirrels in order to estimate the probability that a squirrels food storage will survive through the winter. based on data gathered across several years, the biologists report that the probability a squirrel will successfully store its food is equal to 0.82. from this information, along with what you know about probability, which one of the following statements is correct?

because probabilities cannot be greater than 1 or negative, 0.82 is a legitimate probability.

because probabilities can only be 0.5 or smaller, 0.82 is not a legitimate probability.

because the number 0.82 was based on past data, it should be called a prediction instead of being called a probability.

because a probability of 0.82 is equivalent to a percentage of 82%, and because 82 is larger than 1, it is impossible for a probability to equal 0.82.

because the value 0.82 was calculated from a sample, it is a statistic and not a true probability.

Accepted Answer

# Brief Explanations:
Probability values range from $0$ (impossible event) to $1$ (certain event). A probability of $0.82$ is within this range ($0\leqslant P(A)\leqslant1$).
- Option 1: Probabilities $P$ satisfy $0\leqslant P\leqslant1$. Since $0 < 0.82<1$, $0.82$ is a legitimate probability.
- Option 2: Probabilities can be greater than $0.5$. For example, if it is very likely that an event occurs (e.g., the probability of getting a non - tail when flipping a fair coin is $0.5$, and if an event is more likely, its probability can be higher).
- Option 3: A probability calculated from past data (empirical probability) is still a valid probability. Probability can be estimated from data.
- Option 4: When converting a probability to a percentage, we multiply by $100$. So $0.82\times100 = 82\%$. The probability value itself ($0.82$) is between $0$ and $1$, and the percentage is just a re - scaling.
- Option 5: A statistic is a numerical characteristic of a sample. An empirical probability (calculated from a sample) is still a type of probability.

# Answer:
Because probabilities cannot be greater than 1 or negative, 0.82 is a legitimate probability.

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