As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 30%, what is the probability that Karen will be accepted to at least one project?
Choose the most appropriate option
A) 729/1000 B) 657/1000 C) 343/500 D) 123/250 E) 17/100
Since the probability of Karen's being accepted to each individual project is 30%, the probability of her not being accepted to each project is 70%. The probability that she will be accepted to none is, therefore, (7/10)*(7/10)*(7/10)=343/1000.   P(Karen will be accepted to at least one project) = 1 - (343/1000) = 657/1000.   The answer is 657/1000.
<result>B</result>
As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 30%, what is the probability that Karen will be accepted to at least one project?