Abag of 25 tulip bulbs contains 10 red tulip bulbs, 8 yellow tulip bulbs, and 7 purple tulip bulbs. (a) what is the probability that two randomly selected tulip bulbs are both red? (b) what is the probability that the first bulb selected is red and the second yellow? (c) what is the probability that the first bulb selected is yellow and the second red? (d) what is the probability that one bulb is red and the other yellow?

A bag of 25 tulip bulbs contains:

Use theoretical definition of probability:

1. What is the probability that two randomly selected tulip bulbs are both red?

The number of favorable outcomes is the number of ways to select 2 red bulbs from 10 red bulbs:

The number of possible outcomes is the number of ways to select 2 bulbs from 25 bulbs:

Then

2. What is the probability that the first bulb selected is red and the second yellow?

The probability to select 1st bulb red is the probability to select second bulb yellow is (only 24 bulbs left).

Then use the product rule:

3. What is the probability that the first bulb selected is yellow and the second red?

The probability to select 1st bulb yellow is the probability to select second bulb red is .

Then use the product rule:

4. What is the probability that one bulb is red and the other yellow?

Two cases are possible: 1st-red, 2nd - yellow or 1st - yellow, 2nd - red. Then use the addition rule: