Question

Ten percent of U.S. households contain $5$or more people. You want to simulate choosing a household at random and recording whether or not it contains $5$or

more people. Which of these are correct assignments of digits for this simulation? (a) Odd = Yes ($5$or more people); Even = No (not $5$or more people)

(b) $0$= Yes; $1,2,3,4,5,6,7,8,9$= No

(c) $5$= Yes; $0,1,2,3,4,6,7,8,9$= No

(d) All three are correct.

(e) Choices (b) and (c) are correct, but (a) is not.

Short answer

The choices (b) and (c) are correct, but (a) is not.

Step-by-step solution

Step 1. Given Information    

percent of homes in the United States with $5$or more individuals = $10\%$ For this simulation, we must determine the correct digit assignments:

Step 2. Concept Used  

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$(never happens) and $1$(happens frequently) (always occurs).

Step 3. Explanation   

We will check each of the given options.

a) The $5$out of the 10 digits result in $5$or more people, resulting in a probability of $50\%$instead of $10\%$Hence, it is incorrect.

b)The $1$out of the $10$digits result in $5$or more people, resulting in a probability of $10\%$Hence, it is correct.

(c) The $1$out of the $10$digits result in $5$or more people, resulting in a probability of $10\%$Hence, it is correct.

(d) Incorrect as we already know (a) is incorrect. (e) correct because (b) and (c) are correct and (a) is incorrect.