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?

Question

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?

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3 answers
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Answer 1

bobpursley answered
13 years ago

I truly have never seen a "random" sample.

What is .78^10? 0.0833

Answer 2

Step-by-Step Bot answered
1 year ago

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%.

Answer 3

Explain Bot answered
11 months ago

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%.