if 18% of all Americans are underweight, find the probability that if three Americans are selected at random all will be underweight.

make a chart

UW .18

Not UW .82

.18 x .18 x .18 = .005832

.5832%

Well, we're diving into some statistics here. Let's see. If 18% of all Americans are underweight, that means the probability of randomly selecting an underweight American is 0.18. So, for the first American, the probability is 0.18. Now, assuming we put the first American back and repeat the selection process, the probability for the second American being underweight is also 0.18. The same goes for the third American.

Since we're dealing with independent events, we can multiply the probabilities together: 0.18 * 0.18 * 0.18 = 0.059%.

So, the probability that if three Americans are selected at random, all of them will be underweight, is approximately 0.059%. Or in other words, quite a slim chance.

To find the probability that all three randomly selected Americans will be underweight, we need to calculate the probability of selecting an underweight American for each of the three selections, and then multiply those probabilities together.

Given that 18% of all Americans are underweight, the probability of selecting an underweight American on the first selection is 0.18 (or 18%).

For the second selection, since the selections are done without replacement, the probability of selecting another underweight American will depend on the outcome of the first selection. So, for the second selection, the probability of selecting an underweight American is now 0.18 * (the probability that the first selection was an underweight American).

Similarly, for the third selection, the probability of selecting an underweight American is 0.18 * (the probability that both the first and second selections were underweight Americans).

Let's calculate it step by step:

Step 1: Probability of selecting an underweight American on the first selection = 0.18

Step 2: Probability of selecting an underweight American on the second selection = 0.18 * (probability that the first selection was underweight)

Since there are no replacements, the probability that the first selection was underweight is still 0.18.

So, the probability of selecting an underweight American on the second selection = 0.18 * 0.18 = 0.0324

Step 3: Probability of selecting an underweight American on the third selection = 0.18 * (probability that the first and second selections were underweight)

Since there are no replacements, the probability that both the first and second selections were underweight is still 0.18 * 0.18 = 0.0324.

So, the probability of selecting an underweight American on the third selection = 0.18 * 0.0324 = 0.00585

Therefore, the probability that all three randomly selected Americans will be underweight is 0.00585 (or approximately 0.59%).

To solve this problem, we can use the concept of probability and the assumption that each American is selected randomly and independently of one another.

Let's break down the problem step by step:

Step 1: Find the probability of selecting one underweight American.
Given that 18% of all Americans are underweight, the probability of selecting an underweight American is 0.18.

Step 2: Calculate the probability of selecting three underweight Americans in a row.
Since the selection of Americans is assumed to be independent, we can multiply the probabilities together. So the probability of selecting three underweight Americans in a row is calculated as follows:
P(underweight, underweight, underweight) = P(underweight) * P(underweight) * P(underweight)
= (0.18) * (0.18) * (0.18)
≈ 0.005832

So, the probability that if three Americans are selected at random, all three will be underweight is approximately 0.005832, or about 0.5832%.