1. (10 points) A bin of 35 manufactured parts contains 6 defective parts and 29
ID: 3206926 • Letter: 1
Question
1. (10 points) A bin of 35 manufactured parts contains 6 defective parts and 29 non-defective parts. A sample of size 5 parts is selected from 35 parts. Selected parts are not replaced. How many different samples are there of size five that contain exactly 2 defective parts? What is the probability that a sample contains exactly 2 defective parts? 2. (5 points) Out of 5 candidates, we would like to choose a manager, an assistant manager and a secretary. In how many ways we can do that? 3. (5 points) How many different signals, each consisting of 9 flags hung in a line, can be made from a set of 4 white flags, 3 red flags, and 2 blue flags if all flags of the same color are identical?Explanation / Answer
There are 3 questions. Answering 1st question. Please post other questions separately.
1. Since sample of 5 bins is taken out without replacement. So 1st sample can be taken out in 35 possible ways, 2nd can be done in 34 and with same way 5th sample can be taken out in 31 possible ways. Since arrangement doesn't matter. So we divide it by 5! as well. It's clear combination problem. hence total possible outcome =
nCk = n!/(k!*(n-k)! = 35!/(5!*30!) = 324632
Number of Sample with exactly 2 defective pieces = sample of 2 defective pieces out of 6 defective + sample of 3 non defective pieces out of total 29 = 6C2+29C3 = 6!/2!4! * 29!/26!3! = 15 * 3654 = 54810
Probability of exactly 2 defective pieces = number of sample with exactly 2 defective pieces/total number of samples = 54810/324632 = 0.169
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.