Assume that you are a member of a small class of 50 students (30 males and 20 fe
ID: 3134667 • Letter: A
Question
Assume that you are a member of a small class of 50 students (30 males and 20 females). Suppose I wish to select 10 students to take part in a survey. In how many different ways can I select my 10 students? In how many different ways can I select 5 males and 5 females? What is the probability that I select 5 males and 5 females? Suppose I select the 10 students using a simple random sample. What is the probability that you are one of the 10 students? Are you a male or a female? Suppose instead I randomly select 5 of the males and 5 of the females. What is the probability that you are one of the 10 students?Explanation / Answer
a) Ans: 10 student can be selected in 50C10 = 10272278170 ways.
b) Ans: 5 males and 5 females, out of 30 males and 20 females can be selected
in 30C4*20C5 =142506*15504 = 2209413024 ways.
c) Ans. The probability of selecting 5 males and 5 females, out of 30 males and 20 females is
(30C5*20C5)= /50C10= 2209413024/10272278170 = 0.2151.
d) Ans. A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. Asimple random sample is meant to be an unbiased representation of a group. Therefore, the probability of selecting me among the 10 student is 10/ 50 = 0.20.
e) Ans. I am a male.
f) Ans. The probability of selecting me is 1. The remaining probability are 4 out of 29 males and 5 out of 20 female. The required probability is (1*29C4*20C5)= /50C10= 368235504/10272278170 = 0.0358.