Questions: The projected population (in thousands) by race for a certain country in 2025 and 2050 is given in the table. Find the probability that a randomly selected person in the given year is of the race specified. Complete parts a through d below. Race 2025 2050 White 207,484 207,555 Hispanic 56,835 91,701 Black 40,771 55,304 Asian and Pacific Islander 18,352 34,383 Multiracial or other 2167 3893 (a) Hispanic in 2025 0.1745 (Round to four decimal places as needed.) (b) Hispanic in 2050 (Round to four decimal places as needed.)

Solution Steps

To find the probability that a randomly selected person in the given year is of the specified race, we need to divide the population of the specified race by the total population for that year.

For part (b), we will calculate the probability for a Hispanic person in 2050.

1. Sum the populations of all races for the year 2050.
2. Divide the population of Hispanic people by the total population for 2050.
3. Round the result to four decimal places.

To find the total population in 2050, we sum the populations of all races:

\[ \text{Total Population}_{2050} = \text{White}_{2050} + \text{Hispanic}_{2050} + \text{Black}_{2050} + \text{Asian and Pacific}_{2050} + \text{Multiracial or Other}_{2050} \]

Substituting the values:

\[ \text{Total Population}_{2050} = 207555 + 91701 + 55304 + 34383 + 3893 = 392836 \]

The probability \( P \) that a randomly selected person in 2050 is Hispanic is given by:

\[ P(\text{Hispanic}) = \frac{\text{Hispanic}_{2050}}{\text{Total Population}_{2050}} \]

Substituting the values:

\[ P(\text{Hispanic}) = \frac{91701}{392836} \approx 0.2334 \]

Final Answer