A bag of 27 tulip bulbs contains 11 red tulip bulbs, 9 yellow tulip bulbs, and 7 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? (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) The probability that both bulbs are red is nothing.

(a) The probability that the two randomly selected tulip bulbs are both red is 0.1567.

(b) The probability that the first bulb selected is red and the second yellow is 0.1410.

(c) The probability that the first bulb selected is yellow and the second red is 0.1410.

(d) The probability that one bulb is red and the other yellow is 0.2820.

Step-by-step explanation:

The probability of an event E is defined as:

, here n (E) = favorable outcomes and N =total no. of outcomes.

Denote the events as follows:

R = a red tulip bulb is selected.

Y = a yellow tulip bulb is selected.

P = a purple tulip bulb is selected.

The information provided is:

N = total number of tulip bulbs = 27

n (R) = number of red tulip bulbs = 11

n (Y) = number of yellow tulip bulbs = 9

n (P) = number of purple tulip bulbs = 7

Two tulip bulbs are randomly selected.

(a)

Compute the probability that both tulip bubs are red as follows:

P (2 tulip bulbs being red) = P (1st bulb is red) × P (2nd bulb is red)

Thus, the probability that the two randomly selected tulip bulbs are both red is 0.1567.

(b)

Compute the probability that the first bulb selected is red and the second yellow as follows:

P (1st is red & 2nd is yellow) = P (1st bulb is red) × P (2nd bulb is yellow)

Thus, the probability that the first bulb selected is red and the second yellow is 0.1410.

(c)

Compute the probability that the first bulb selected is yellow and the second red as follows:

P (1st is yellow & 2nd is red) = P (1st bulb is yellow) × P (2nd bulb is red)

Thus, the probability that the first bulb selected is yellow and the second red is 0.1410.

(d)

Compute the probability that one bulb is red and the other yellow as follows:

P (1 red and 1 yellow) = P (1st is yellow & 2nd is red)

                                                     + P (1st is red & 2nd is yellow)

                                   = 0.1410 + 0.1410

                                    = 0.2820

Thus, the probability that one bulb is red and the other yellow is 0.2820.