A bag of 100 tulip bulbs purchased from a nursery contains 20 red tulip bulbs, 25 yellow tulip bulbs, and 55 purple tulip bulbs. (c) Select the correct choice below and fill in the answer boxes within your choice. (Type whole numbers.) A. If 100 tulip bulbs were sampled with replacement, one would expect about of the bulbs to be red and about of the bulbs to be purple. B. If 100 tulip bulbs were sampled with replacement, one would expect exactly of the bulbs to be red and exactly of the bulbs to be purple.
Solution
Step 1 ：The problem is asking for the expected number of red and purple tulip bulbs if 100 tulip bulbs were sampled with replacement. This is a problem of probability.
Step 2 ：The probability of drawing a red tulip bulb is \(\frac{20}{100} = 0.2\) and the probability of drawing a purple tulip bulb is \(\frac{55}{100} = 0.55\).
Step 3 ：Since we are sampling with replacement, each draw is independent and the probabilities do not change.
Step 4 ：Therefore, if we draw 100 times, we would expect to get about \(0.2 \times 100 = 20\) red tulip bulbs and \(0.55 \times 100 = 55\) purple tulip bulbs.
Step 5 ：Final Answer: If 100 tulip bulbs were sampled with replacement, one would expect about \(\boxed{20}\) of the bulbs to be red and about \(\boxed{55}\) of the bulbs to be purple.
