Question

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.

Answer 1

Answer:

(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:

$P(E)=\frac{n(E)}{N}$, 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)

                                           $=\frac{11}{27}\times \frac{10}{26}\\=0.1567$

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)

                                               $=\frac{11}{27}\times \frac{9}{26}\\=0.1410$

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)

                                               $=\frac{9}{27}\times \frac{11}{26}\\=0.1410$

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.