Work each problem. U.S. Population Origins Projected...

Work each problem. U.S. Population Origins Projected Hispanic/Latino and non-Hispanic/Latino U.S. populations (in thousands) for 2025 are given in the following table. (table cannot copy) Assume that these projections are accurate. Estimate the probability that a U.S. resident selected at random in 2025 is A. Hispanic/Latino. B. not white. C. Native American or black. D. What are the odds that a randomly selected U.S. resident is Asian?

Work each problem.
U.S. Population Origins Projected Hispanic/Latino and non-Hispanic/Latino U.S. populations (in thousands) for 2025 are given in the following table.
(table cannot copy)
Assume that these projections are accurate. Estimate the probability that a U.S. resident selected at random in 2025 is
A. Hispanic/Latino.
B. not white.
C. Native American or black.
D. What are the odds that a randomly selected U.S. resident is Asian?

Key Concepts

Probability

Probability is a measure of the likelihood of an event occurring, typically calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes within a defined sample space. It is fundamental to quantifying uncertainty using population data or any data set.

Relative Frequency

Relative frequency is the practical method of estimating probability by using actual data counts from the population (or sample) compared to the total count. It frames probability as an empirical ratio, especially useful when dealing with projected or observed data.

Odds

Odds describe the ratio of the probability that an event occurs to the probability that it does not occur. Unlike probability, which is expressed as a fraction or percentage of occurrence, odds provide a comparative measure and are calculated by dividing the event's probability by one minus that probability.

Addition Rule for Mutually Exclusive Events

This rule states that if two events cannot occur simultaneously, the probability of either event occurring is the sum of their individual probabilities. This is vital when the event of interest is defined as the occurrence of at least one in a set of distinct outcomes, such as separate population groups.

Transcript

00:01 For this exercise, we need to reference the table given that shows the projected number of, in the u .s.

00:09 Population, in thousands, in certain ethnic groupings, hispanic latino, white, black, native american, or asian.

00:18 Now, before we can do the probabilities that are listed in this problem, we need to know the size of our sample set.

00:24 How many people are in this chart in all? well, if we add up all of the numbers given here, our sample set size is 335 ,050.

00:36 So as we're doing our probabilities, we'll be referencing this number as our total population.

00:42 So first, what is the probability that if i pick somebody at random, they will be in the hispanic latino population group? well, if i look at the chart, there are 58 ,930 people in that particular group out of 335 ,050.

01:09 Putting that in my calculator gives me 0 .176.

01:14 And usually for fractions like this, it's common to put them as a decimal because the fraction is very bulky and awkward to work with.

01:22 So the probability of picking somebody in the hispanic latino group is 0 .176.

01:30 Well, second, what is the probability of picking somebody who is not in the white category? well, that is the complement of somebody being in the white category.

01:45 So i could find one minus the probability of showing up is a white in the white category.

01:55 Well, according to our chart, there are 209 ,117 in that population compared to our total population size of 335 ,050.

02:07 Now, i'm going to put this into my calculator.

02:10 One minus this fraction gives me a value of 0 .376.

02:17 Okay.

02:18 Next, what is the probability of being either native american or black? well, when we have an or in probability, we are going to be adding.

02:37 So i'm going to find the probability of being a native american.

02:40 I'm going to abbreviate that just to make this a little bit more compact...

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