Question

What equation is needed to show why the count is 675? Also when finding the rest of probabilities would your totaly divide be 2300 or change for each one?

Part B: Sampling and Random Variable You already have ten marked pennies (ones with numbers from Part A) and 15 unmarked pennies. Thought experiment: Throw them all in a jar and shake. Without looking, pull three out and record how many of them are marked (have a number). You will get 0, 1, 2, or 3 marked coins. How many different samples of 3 pennies out of 25 can you get? (Order doesn't matter.) Answer: 2,300 Show why 2,300 is the answer. How many of those samples would have 0, 1, 2, 3 marked coins? #of marked pennies in sample 0 455 1,050 1 (Show why this count should be 675.) 2 675 3 120 (Notice this total matches the total above.) Total 2,300 If you draw a simple random sample of size 3, each sample is equally likely. Counting the number of marked coins gives us discrete random variable, X. a 455/2,300 1978 P(X-0)= P(X=1)= 1,650/2, B00 P(X=2)= P(X-3)= Find the rest of these probabilities. Then find the mean and standard deviation of this discrete random variable. o25/2, 300 120/a,300 three

Answer 1

so you select 3 pennies out of 25
10 marked and 15 unmarked

total number of different sample = 25C3
= 25 *24*23/6
= 2300

X = number of marked pennies
number of ways to get x marked pennies
= 10Cx * 15C(3-x)

if x = 2
10C2 * 15C1 = 45 * 15 = 675

P(X = k) = 10Ck * 15C(3-k)/25C3

for probabilities we divide by 2300 as it is the total number of different sample