(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
[tex]\dfrac{5}{13}\cdot\dfrac{9}{25}=\dfrac{9}{65}[/tex]
(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
[tex]\dfrac{5}{13}\cdot\dfrac{9}{25}=\dfrac{9}{65}[/tex]
(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
[tex]\dfrac{9}{26}\cdot\dfrac{10}{25}=\dfrac{9}{65}[/tex]
(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.
