A bag of 25 tulip bulbs contains 10 red tulip bulbs, 9 yellow tulip bulbs, and 6 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag.
(a) What is the probability that the two randomly selected tulip bulbs are both red?
(b) What is the probability that the first bulb selected is red and the second yellow?
© 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) The probability that both bulbs are red is 0.15 .
(Round to three decimal places as needed.)
(b) The probability that the first bulb is red and the second is yellow is 0.15 .
(Round to three decimal places as needed.)
© The probability that the first bulb is yellow and the second is red is
(Round to three decimal places as needed.)

Question

UpStudy AI · Accepted Answer

**(a) Both bulbs are red**

The probability that the first bulb is red is  
$$
\frac{10}{25}.
$$  
Once a red bulb is selected, there are 9 red bulbs left and a total of 24 bulbs remaining, so the probability that the second bulb is red is  
$$
\frac{9}{24}.
$$  
Multiplying these, the probability that both bulbs are red is  
$$
\frac{10}{25} \times \frac{9}{24} = \frac{90}{600} = 0.150.
$$

---

**(b) First bulb red, second yellow**

The probability that the first bulb is red is  
$$
\frac{10}{25}.
$$  
After selecting a red bulb, there are 9 yellow bulbs left out of 24 bulbs, so the probability that the second bulb is yellow is  
$$
\frac{9}{24}.
$$  
Thus, the probability that the first is red and the second yellow is  
$$
\frac{10}{25} \times \frac{9}{24} = \frac{90}{600} = 0.150.
$$

---

**(c) First bulb yellow, second red**

The probability that the first bulb is yellow is  
$$
\frac{9}{25}.
$$  
If a yellow bulb is selected first, there are still 10 red bulbs remaining out of 24 bulbs, so the probability that the second bulb is red is  
$$
\frac{10}{24}.
$$  
Thus, the probability that the first is yellow and the second red is  
$$
\frac{9}{25} \times \frac{10}{24} = \frac{90}{600} = 0.150.
$$

---

**(d) One bulb is red and the other yellow**

There are two mutually exclusive cases:
- First red then yellow (from part (b)): $$0.150$$
- First yellow then red (from part (c)): $$0.150$$

So, the total probability is  
$$
0.150 + 0.150 = 0.300.
$$
**(a) Both bulbs are red: 0.150** **(b) First bulb red, second yellow: 0.150** **(c) First bulb yellow, second red: 0.150** **(d) One bulb is red and the other yellow: 0.300**

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