Ali surveyed 200 students at a school and recorded the eye color and the gender of each student. of the 80 male students who were surveyed, 60 had brown eyes. if eye color and gender are independent, how many female students surveyed would be expected to have brown eyes?

James adds two numbers a + b. sally adds the same two numbers but reverse the order b + a what property of addition assures us that james and sally will get the same sum

An investment decreases in value by 30% in the first year and decreases by 40% in the second year. what is the percent decrease in percentage in the investment after two years

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?