Abag of 26 tulip bulbs contains 10 red tulip bulbs, 9 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)

You have a 10/26=5/13 chance of picking a red bulb with the first try. If you succeed, you'll have 25 bulbs remaining, 9 of which will be red, leading to a probability of 9/25 for the second pick to be red.

This means that the probability of picking two consecutive reds is

(b)

All the other answers will follow the same logic: you have again a 5/13 probability of picking a red bulb as the first bulb, then you'll have 25 remaining bulbs, 9 of which will be yellow. So, the probability of picking a red and then a yellow bulb is again

(c)

You'll have 9 yellow bulbs out of 26 with the first pick, and 10 red bulbs out of 25 with the second pick. So, the probability of picking a yellow and then a red is

(d)

Putting together (b) and (c), we can see that the probability of having a red and a yellow bulb is 9/65, no matter in which order the red and the yellow will appear.