Question: There are 15 blue balls and 5 red balls in a hat. Let p^ be the proportion of red balls in a sample of 5 balls with replacement.
Find Pr(p^=>4/5)
For this would we use the sampling method for p^ or the binomial distribution.
I.e is it
((5c4)(15c1))/(20c5) + ((5c5)(15c0)/(20c5) = 1/204 ~0.0049
or
X ~ (5,0.25)
Pr(X=4) + Pr(X=5) = 0.015625
I've always considered it to be the sampling method where you have to divide the number of ways it can occur by the total number of possible samples. However, in the 2016 VCAA exam 2 Question 3D they simply used the binomial distribution instead of, say, finding the expected number of laptops with a battery life less than 3 hours and then using the above sampling method somehow.