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

Explanation:

Step1: Recall the probability formula

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of elements in event \(A\) and \(n(S)\) is the number of elements in the sample space.

Step2: Identify values for part (b)

For part (b), \(n(A)\) (number of purple tulip bulbs) is \(40\), and \(n(S)\) (total number of tulip bulbs) is \(100\).

Step3: Calculate the probability

Using the formula \(P(\text{purple})=\frac{40}{100} = 0.4\)

Answer:

(a) \(0.4\)
(b) \(0.4\)
(c) The probability of \(0.4\) for both red and purple tulip bulbs means that if we were to select tulip bulbs many times (in a random and independent way), about \(40\%\) of the selections would result in a red tulip bulb and about \(40\%\) would result in a purple tulip bulb.