Question

a bag of 100 tulip bulbs purchased from a nursery contains 30 red tulip bulbs, 35 yellow tulip bulbs, and 35 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 0.3 (type an integer or a decimal. do not round.) (b) the probability that a randomly selected tulip bulb is purple is 0.35 (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.) 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

Explanation:

Step1: Recall probability formula

The probability $P(E)$ of an event $E$ is given by $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of elements in the event $E$ and $n(S)$ is the number of elements in the sample - space. Here, $n(S) = 100$ (total number of tulip bulbs).

Step2: Calculate probability of red tulip

For red tulips, $n(E)=30$. So, $P(\text{red})=\frac{30}{100}=0.3$.

Step3: Calculate probability of purple tulip

For purple tulips, $n(E) = 35$. So, $P(\text{purple})=\frac{35}{100}=0.35$.

Step4: Interpret probabilities

The probability of an event represents the long - run relative frequency of the event. If we sample 100 tulip bulbs with replacement many times, on average, the proportion of red bulbs in the samples will approach 0.3 and the proportion of purple bulbs will approach 0.35. So, if 100 tulip bulbs were sampled with replacement, one would expect about 30 of the bulbs to be red and about 35 of the bulbs to be purple.

Answer:

(a) 0.3
(b) 0.35
(c) A. If 100 tulip bulbs were sampled with replacement, one would expect about 30 of the bulbs to be red and about 35 of the bulbs to be purple.