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 (type an integer or a decimal. do not round.)

Explanation:

Step1: Recall probability formula

The probability $P(E)$ of an event $E$ is given by $P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Calculate probability of red tulip

The total number of tulip bulbs is $n = 100$, and the number of red tulip bulbs is $n_{red}=30$. So, $P(\text{red})=\frac{n_{red}}{n}=\frac{30}{100} = 0.3$.

Step3: Calculate probability of purple tulip

The number of purple tulip bulbs is $n_{purple}=35$. So, $P(\text{purple})=\frac{n_{purple}}{n}=\frac{35}{100}=0.35$.

Step4: Interpret probabilities

The probability that a randomly - selected tulip bulb is red is $0.3$. This means that if we were to select a tulip bulb many times, about 30% of the time we would select a red tulip bulb. The probability that a randomly - selected tulip bulb is purple is $0.35$, which means that about 35% of the time we would select a purple tulip bulb if we made many selections.

Answer:

(a) 0.3
(b) 0.35
(c) The probability 0.3 means that in repeated random selections of a tulip bulb, about 30% of the time a red tulip bulb will be chosen. The probability 0.35 means that in repeated random selections of a tulip bulb, about 35% of the time a purple tulip bulb will be chosen.