Question

A bag 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?

Answer 1

(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

$\dfrac{5}{13}\cdot\dfrac{9}{25}=\dfrac{9}{65}$

(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

$\dfrac{5}{13}\cdot\dfrac{9}{25}=\dfrac{9}{65}$

(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

$\dfrac{9}{26}\cdot\dfrac{10}{25}=\dfrac{9}{65}$

(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.