could you help me with this problem?

Question

You are getting ready to remodel your kitchen and have narrowed down your choices to the following:

For the walls, you can choose from teal, tan, blue or navy. For the trim, you can choose white or beige. For the countertops, you can choose, pearl, peach, or cream.

A) How many points are in the sample space?

B) What is the probability that you will choose teal walls and pearl countertops?

C) What is the probability that you will choose teal walls OR pearl countertops?

D) What is the probability that you will choose tan walls with white trim?

E) What is the probability that none of the options includes navy walls?

Answer 1

4 choices for walls * 2 choices for trim * 3 choices for countertops = 24

next list all 24 possible sample spaces which will enable you to answer the remaining questions.

{teal,white,pearl},{teal, white, peach}, {teal, white, cream}

{teal,beige,pearl}.{teal,beige,peach}, {teal,beige,cream}

{tan,white,pearl},{tan, white, peach}, {tan, white, cream}

{tan,beige,pearl}.{tan,beige,peach}, {tan,beige,cream}

{blue,white,pearl},{blue white, peach}, {blue, white, cream}

{blue,beige,pearl}.{blue,beige,peach}, {blue,beige,cream}

{navy,white,pearl},{navy,white, peach}, {navy, white, cream}

{navy,beige,pearl}.{navy,beige,peach}, {navy,beige,cream}

b) teal walls and pearl countertops. Look in the sample space for how many have teal walls and pearl countertops. You should find 2. Probability = number of desired outcomes (2)/possible outcome (24) = 2/24 = 1/12

c) teal walls or pearl countertops. Look in sample space for how many have teal walls or pearl countertops. You should find 12. Probability = 12/24 = 1/2

d) tan walls and white trim. Look in the sample space for how many with tan walls and white trim. You should find 3. Probability = 3/24 = 1/8

e) none of the options include navy walls. Look in the sample sample for how many not navy walls. You should find 18. Probability = 18/24 = 3/4.