A survey group of 5 students are chosen at random from 25 elementary students and 13 high school students. Determine the probability that at least 2 students chosen are elementary students.
in Statistics Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

There are 38 students in total. The probability, p, of choosing an elementary student=25/38, and the probability of not choosing an elementary student, 1-p,  is 13/38. This is a binomial situation expressed by (p+(1-p))^5 (=1, certainty) which expands to: p^5+5p^4(1-p)+10p^3(1-p)^2+10p^2(1-p)^3+5p(1-p)^4+(1-p)^5. Each term has a meaning: p^5 is the probability of selecting 5 elementary students; 5p^4(1-p) the probability of exactly 4 elementary and one high school student; etc. The probability of at least 2 elementary students is the sum of the probabilities of exactly 2, 3, 4 or 5 elementary students; or it is 1 minus (sum of the probabilities of all high school and exactly one elementary school student)=1-(1-p)^5-5p(1-p)^4=1-(13/38)^5-5*25/38(13/38)^4=0.95026 or 95.03% approx.

by Top Rated User (1.2m points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,516 questions
100,279 answers
2,420 comments
731,779 users