There are 3 red, 6 blue, 5 yellow, and 4 green hair bands in a bag. Tatianna wants a blue hairband and a yellow hairband to wear with her school uniform. What is the probability of picking a yellow hairband followed by a blue hairband, if the first hairband drawn is not replaced?

[tex][/tex] To find the probability of picking a yellow hairband followed by a blue hairband without replacement, we'll first calculate the probability of picking a yellow hairband and then a blue hairband.

Total number of hairbands = 3 (red) + 6 (blue) + 5 (yellow) + 4 (green) = 18

Probability of picking a yellow hairband first:

P(Yellow) = (Number of yellow hairbands) / (Total number of hairbands)

= 5 / 18

After picking a yellow hairband, there are now:

- 17 hairbands left in the bag.

Probability of picking a blue hairband after picking a yellow hairband:

P(Blue | Yellow) = (Number of blue hairbands left) / (Total hairbands left)

= 6 / 17

Now, we can find the probability of picking a yellow hairband followed by a blue hairband:

P(Yellow and then Blue) = P(Yellow) P(Blue | Yellow)

= (5 / 18) (6 / 17)

≈ 0.098

So, the probability of picking a yellow hairband followed by a blue hairband, without replacement, is approximately 0.098 or 9.8%.