If 20% of population have blue eyes, and 5 people are selected at random, what is the probability that at least 4 of them have blue eyes?
HOW DO I FIND THE SOLUTION TO THIS PROBLEM?
Prob(blue eyes) = .2
Prob(not blue eyes)= .8
prob( at least 4 of 5 have blue eyes)
= prob(exactly 4 of 5 have blue eyes) + prob(exactly 5 of 5 have blue eyes)
= C(5,4)(.2)^4 (.8) + C(5,5)(.2)^5
= 5(.0016)(.8) + 1(.00032)
= .000672
In the United States , 60% of the population have brown eyes.
In the United States , 60% of the population have brown eyes.
If 37 people were randomly selected. Find the probability that exactly 22 of them will have brown eyes.
To find the solution to this problem, you can use the concept of probability. Let's break it down step-by-step:
1. Determine the total number of people in the population: Let's say the total population is represented by "N".
2. Calculate the number of people with blue eyes: Since 20% of the population has blue eyes, the number of people with blue eyes can be calculated as 0.20 * N, denoted as "B".
3. Determine the number of people without blue eyes: The number of people without blue eyes can be calculated as N - B, denoted as "N - B".
4. Apply the concept of combination: To find the probability of selecting a specific number of people with blue eyes in a random sample, you can use the concept of combination. The formula for combination is given by C(n, r) = n! / (r!(n - r)!), where n is the total number of people and r is the number of people with blue eyes selected in the random sample.
5. Calculate the probability of at least 4 people with blue eyes: To find the probability of at least 4 people with blue eyes, you need to calculate the probabilities for selecting exactly 4, exactly 5 people with blue eyes, and sum them up.
The overall steps to find the solution to this problem are:
1. Determine the total number of people in the population, "N".
2. Calculate the number of people with blue eyes, "B".
3. Calculate the number of people without blue eyes, "N - B".
4. Calculate the probability of selecting 4 people with blue eyes:
- Calculate the probability of selecting exactly 4 people with blue eyes using the combination formula.
- Multiply this probability by the probability of selecting exactly (5-4) people without blue eyes.
- Calculate the product.
5. Calculate the probability of selecting 5 people with blue eyes:
- Calculate the probability of selecting exactly 5 people with blue eyes using the combination formula.
- Calculate the product.
6. Sum up the probabilities calculated in steps 4 and 5 to get the final probability of selecting at least 4 people with blue eyes.
By following these steps, you will be able to find the solution to the probability problem.