You are adding Badger-themed bedazzle to your striped overalls and are using both red and white beads. You are interested in how the size of the bag of beads you select your beads from changes the probability of outcomes of interest. Compute the probability for outcomes a and b using three different sampling strategies each time. (Small Pop) drawing without replacement from a small population where the bag of beads contains 7 White beads and 3 Red beads. (Large Pop) drawing without replacement from a large population where the bag of beads contains 700 White beads and 300 Red beads. (Same Pop) drawing from a population where the bag of beads always contains 70% White and 30% Red beads. Example: Consider choosing 3 beads. Calculate the probability of selecting no white beads. Small Pop: P([RRR])= 1.1.= 0.008333333 Large Pop: P([RRR])=1000 = 0.02681098 Same Pop: P([RRR])=0.30..30.30 = 0.027 a. Consider choosing 3 beads. Calculate the probability of selecting exactly 1 white bead. Small Pop: Large Pop: Same Pop:
b. Consider choosing 3 beads. Calculate the probability of selecting at least 1 white bead. Small Pop: Large Pop: Same Pop:
c. Consider sampling without replacement.
Does drawing from a population that is small or large relative to your sample size result in a probability that is closest to the probability when sampling with replacement?