You are randomly selecting 10 college students for an experiment. The population in which you are sampling has 78% of the students classified as Caucasian and 22% classified as Minority. What is the probability that all 10 students selected will be Caucasian?
I truly have never seen a "random" sample.
What is .78^10? 0.0833
To calculate the probability that all 10 students selected will be Caucasian, we need to calculate the probability of selecting a Caucasian student for each individual selection, and then multiply these probabilities together.
Given that the population has 78% Caucasian students, the probability of selecting a Caucasian student at random is 0.78.
Since we want to select 10 Caucasian students in a row, we can multiply the probabilities together:
P(Caucasian) for each selection = 0.78
P(all 10 students Caucasian) = 0.78^10
Calculating this, we find:
P(all 10 students Caucasian) ≈ 0.078
So the probability that all 10 students selected will be Caucasian is approximately 0.078, or 7.8%.
To calculate the probability that all 10 students selected will be Caucasian, we need to use the concept of probability and apply it to this specific scenario.
Step 1: Determine the probability of selecting one Caucasian student from the population.
Given that 78% of the students in the population are Caucasian, the probability of selecting one Caucasian student can be calculated as:
P(Caucasian) = 78% = 0.78
Step 2: Since each selection is independent, we can assume that the probability remains the same for each subsequent selection.
Step 3: Calculate the probability of selecting all 10 students as Caucasians.
Since we are selecting 10 students and assuming each selection is independent, we can multiply the probability of selecting a Caucasian student by itself 10 times:
P(all 10 students are Caucasian) = P(Caucasian) * P(Caucasian) * ... * P(Caucasian)
= 0.78 * 0.78 * 0.78 * ... * 0.78 (10 times)
= 0.78^10
Using a calculator or a computer program, we can calculate this value:
P(all 10 students are Caucasian) ≈ 0.1948
Therefore, the probability that all 10 randomly selected students will be Caucasian is approximately 0.1948 or 19.48%.