Answer to Question #340123 in Statistics and Probability for Maneo

Question

Manen’s closet has three pairs of pants (black, white and green), two shirts (green and white) and two pairs of shoes (black and white).

• a) How many different outfits can be made?

• b)   Write down the sample space.

• c)   What is the probability that if you close your eyes and choose randomly, you would   

choose:

• (i) Pants and shoes with the same colour?

• (ii) Pants and shirts with the same colour?

• (iii) Pants, shoes and shirts with the same colour?

• (iv) Pants, shoes and shirts with the different colours?

Answer 1

a)

$$\dbinom{3}{1}\dbinom{2}{1}\dbinom{2}{1}=12$$

12 different outfits can be made.

b) The sample space is

$$S=\{B_1G_2B_3, B_1G_2W_3,B_1W_2B_3,B_1W_2W_3,$$

$$W_1G_2B_3, W_1G_2W_3,W_1W_2B_3,W_1W_2W_3,$$

$$G_1G_2B_3, G_1G_2W_3,G_1W_2B_3,G_1W_2W_3\}$$

c)

(i)

$$B_1G_2B_3,B_1W_2B_3,W_1G_2W_3,W_1W_2W_3$$

$$p=\dfrac{4}{12}=\dfrac{1}{3}$$

(ii)

$$W_1W_2B_3, W_1W_2W_3, G_1G_2B_3, G_1G_2W_3$$

$$p=\dfrac{4}{12}=\dfrac{1}{3}$$

(iii)

$$W_1W_2W_3$$

$$p=\dfrac{1}{12}$$

(iv)

$$B_1G_2W_3,W_1G_2B_3,G_1W_2B_3$$

$$p=\dfrac{3}{12}=\dfrac{1}{4}$$