Question

a bag of 100 tulip bulbs purchased from a nursery contains 40 red tulip bulbs, 20 yellow tulip bulbs, and 40 purple tulip bulbs. (a) what is the probability that a randomly selected tulip bulb is red? (b) what is the probability that a randomly selected tulip bulb is purple? (c) interpret these two probabilities. (a) the probability that a randomly selected tulip is red is 0.4 (type an integer or a decimal. do not round.) (b) the probability that a randomly selected tulip bulb is purple is 0.4 (type an integer or a decimal. do not round.) (c) select the correct choice below and fill in the answer boxes within your choice. (type whole numbers.) o a. 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. o b. 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.

Explanation:

Step1: Calculate the number of red bulbs

There are 40 red bulbs out of 100 total bulbs.

Step2: Calculate the probability of red

Probability \(P(\text{red})=\frac{40}{100} = 0.4\)

Step3: Calculate the number of purple bulbs

There are 40 purple bulbs out of 100 total bulbs.

Step4: Calculate the probability of purple

Probability \(P(\text{purple})=\frac{40}{100}=0.4\)

Step5: Interpret the probabilities

Probability is a measure of likelihood. When sampling with replacement, we use the probability as an estimate. Since \(P(\text{red}) = 0.4\) and \(P(\text{purple})=0.4\), for 100 samples, we expect about \(0.4\times100 = 40\) red and about \(0.4\times100=40\) purple.

Answer:

(a) \(0.4\)
(b) \(0.4\)
(c) B. If 100 tulip bulbs were sampled with replacement, one would expect about \(40\) of the bulbs to be red and about \(40\) of the bulbs to be purple.