based on a study by Dr.P. Sorita Soni at Indiana University, we know that the eye colors in the United States are distributed as follows: 42% brown, 35% blue, 11% green, 6% gray, and 6% hazel
b) identify onw factor that might make this particular sample biased and not representative of the general population of people in the United States.
c)If one person is randomly selected, what is the probability that this person will have brown or blue eyes? Express the probability as a decimal value.
d) If two people are randomly selected, what is the probability that at least one of them has a brown eye? Express the probability as a decimal value
b) One factor that might make this particular sample biased and not representative of the general population of people in the United States is the sample size. The study conducted by Dr. P. Sorita Soni at Indiana University might have a relatively small sample size, leading to potential sampling bias. Ideally, a larger sample size would be more representative and provide a more accurate distribution of eye colors in the general population.
c) To find the probability that a randomly selected person will have brown or blue eyes, we need to add the percentages of brown and blue eye colors together.
Probability of brown or blue eyes = Probability of brown eyes + Probability of blue eyes
= 42% + 35%
= 77%
Thus, the probability that a person will have brown or blue eyes is 0.77 or 77%.
d) To find the probability that at least one of the two randomly selected people has a brown eye, we can calculate the complementary probability of neither person having a brown eye and subtract it from 1.
Probability of at least one person having a brown eye = 1 - Probability of both having non-brown eyes
Probability of both having non-brown eyes = Probability of first person having non-brown eyes * Probability of second person having non-brown eyes
= (100% - 42%) * (100% - 42%)
= 58% * 58%
= 33.64%
Therefore, the probability of at least one of the two randomly selected people having a brown eye is approximately 1 - 0.3364 = 0.6636 or 66.36%.