Question

Question 2. Gopal is taking a Probability course, and would like to find a study-partner to discuss concepts that are being covered in his class and brainstorm ideas on applying them in day-to-day scenarios. He feels that the collaboration would be most effective if he finds a study-partner who lives within 5 miles of his residence. Assume that each student in his class has a 0.3 probability of living in his 5-mile neighborhood, independently of other students. 1. What is the probability that there are exactly 10 potential study-partners (i.e. students who are within 5-mile neighborhood of Gopal's home) in his class of 34 students (excluding himself)? 2. What is the probability that Gopal has to ask exactly 5 students in his class before he finds the first person who lives in his neighborhood?

Answer 1

solution : p=0.3 0 X ~ Binomial (34303) P(x) = (x) b*q*-* Plx =10) - (39)0-3) (07) a 10.1483 10 34-10 2 ): Number of student need to ask before first success yn Geometric Ply) = q lp Ply=5 = = 10.7) 10.3) 10.0720