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Explore bird stats with simulations! By assigning digits, scientists mimic populations where 40% have wingspans larger than 10 inches, helping us predict the probability of finding such a bird in a group of six.
In a certain population of birds, about 40 percent of the birds have a wingspan greater than 10 inches. Biologists studying the birds will create a simulation with random numbers to estimate the probability of finding 1 bird in a sample of 6 birds with a wingspan greater than 10 inches. Which of the following assignments of the digits 0 to 9 will model the population?
The best assignment of digits to model the population is:
E. Let the digits from 0 to 4 represent birds with a wingspan greater than 10 inches and the remaining digits represent birds with a wingspan less than or equal to 10 inches.
Here’s why:
- We know that 40% of the birds have a wingspan greater than 10 inches. This translates to 4 out of 10 birds.
- Since we have 10 digits (0-9), we need an assignment that accurately reflects this 40/60 ratio.
- Option A assigns half of the digits (even numbers) to birds with a larger wingspan, but this represents 50%, not 40%.
- Option B assigns only 2 digits (0 and 1) to larger wingspans, representing just 20%, which is too low.
- Option C assigns 3 digits (0-2) to larger wingspans, representing 30%, again not matching the 40%.
- Option D also assigns 3 digits to larger wingspans, leading to 30% representation.
- However, option E perfectly captures the 40% representation by assigning 5 digits (0-4) to larger wingspans.
Therefore, assigning digits 0-4 to birds with a wingspan greater than 10 inches and 5-9 to smaller wingspans accurately reflects the given information about the bird population.
This way, when simulating random samples of 6 birds using these assigned digits, you’ll have a model that better represents the actual probability of finding 1 bird with a wingspan greater than 10 inches in the sample.
What are the Different types of Probability?
Probability can be classified into several types based on the nature of the events and the way probabilities are calculated. Here are some common types of probability:
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Classical Probability: This is based on equally likely outcomes. For example, rolling a fair six-sided die, each outcome (1 through 6) has an equal probability of 1/6.
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Empirical Probability: Also known as experimental probability, it is based on observations or experiments. It involves conducting experiments and recording the outcomes to determine the probability. For example, flipping a coin many times and observing the ratio of heads to tails.
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Subjective Probability: This type of probability is based on an individual’s judgment or belief regarding the likelihood of an event occurring. It is often used in situations where there is no data or when the outcomes are uncertain. For example, a weather forecaster predicting the chance of rain tomorrow based on experience and current weather patterns.
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Conditional Probability: This is the probability of an event occurring given that another event has already occurred. It is denoted by P(A|B), where A and B are events. For example, the probability of drawing a red card from a deck of cards given that a card drawn is a face card.
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Joint Probability: This refers to the probability of the occurrence of two or more events simultaneously. For example, the probability of rolling a 2 on one die and a 3 on another die when rolling two fair six-sided dice.
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Marginal Probability: This is the probability of a single event occurring without any reference to any other event. It is derived from joint probabilities. For example, the probability of rolling a 4 on one fair six-sided die.
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Bayesian Probability: This is a type of probability that represents a degree of belief rather than a frequency or proportion. It incorporates prior knowledge or beliefs about a situation and updates these beliefs based on new evidence using Bayes’ theorem.
These are some of the fundamental types of probability, each with its own application and methods of calculation.
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Categories: Math
