Step 1 :Given that a bag of 100 tulip bulbs contains 20 red tulip bulbs, 25 yellow tulip bulbs, and 55 purple tulip bulbs.
Step 2 :The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes.
Step 3 :In this case, the total number of outcomes is the total number of tulip bulbs, which is 100.
Step 4 :The number of ways the event can occur is the number of red or purple tulip bulbs.
Step 5 :So, to find the probability that a randomly selected tulip bulb is red, we need to divide the number of red tulip bulbs by the total number of tulip bulbs. This gives us \(\frac{20}{100} = 0.2\).
Step 6 :Similarly, to find the probability that a randomly selected tulip bulb is purple, we need to divide the number of purple tulip bulbs by the total number of tulip bulbs. This gives us \(\frac{55}{100} = 0.55\).
Step 7 :Final Answer: The probability that a randomly selected tulip bulb is red is \(\boxed{0.2}\) and the probability that a randomly selected tulip bulb is purple is \(\boxed{0.55}\).