state what each probability represents.

Question

3. A box contains 4 black shirts, 8 blue shirts, 4 black pants, and 10 blue pants. Determine the probability of randomly selecting a blue piece of clothing or a pair of pants. Use this formula 𝑷(𝑨 𝒐𝒓 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) − 𝑷(𝑨 𝒂𝒏𝒅 𝑩) to solve and explain what each probability represents.

a) state what each probability represents. (4 points)

𝑃(𝐵 𝑜𝑟 𝑃) : probability of selecting ______________________________________________ ___________________________________________________________________________

𝑃(𝐵) : probability of selecting __________________________________________________

𝑃(𝑃) : probability of selecting __________________________________________________

𝑃(𝑃 𝑎𝑛𝑑 𝐵) : probability of selecting ____________________________________________

Answer 1

First, let's state what each probability represents:

1. P(B or P): This is the probability of selecting either a blue piece of clothing or a pair of pants.
2. P(B): This is the probability of selecting a blue piece of clothing. The total number of blue pieces of clothing is the sum of blue shirts and blue pants.
3. P(P): This is the probability of selecting a pair of pants. The total number of pants is the sum of black pants and blue pants.
4. P(P and B): This is the probability of selecting a piece of clothing that is both blue and a pair of pants, in other words, blue pants.

Now, let's do the calculations:

1. P(B or P): The number of pieces of clothing that is either blue or a pair of pants is 22 (8 + 4 + 10). The total number of pieces of clothing is 26 (4 + 8 + 4 + 10). So, P(B or P) = 22/26 = 11/13
2. P(B): The number of pieces of blue clothing is 18 (8 + 10). So, P(B) = 18/26 = 9/13
3. P(P): The number of pairs of pants is 14 (4 + 10). So, P(P) = 14/26 = 7/13
4. P(P and B): The number of blue pants is 10. So, P(P and B) = 10/26 = 5/13

Hope you found this helpful.

Answer 2

Blue Blk Total

Shirts 8 4 12

Pants 10 4 14

Total 18 8 26

P(Blue or Pants) = P(Blue) + P(Pants) - P(Blue and Pants) (to avoid double counting)

P(Blue or Pants) = 18/26 + 14/26 - 10/26 = 22/26 = 11/13

Answer 3

P(B or P) = probability of selecting a blue item OR a pair of pants

P(B) = probability of selecting any blue item = 18/26

P(P) = probability of selecting any pair of pants = 14/26

P(P and B) = probability of selecting an item that is both a pair of pants AND blue = 10/26

Using the formula:

P(B or P) = P(B) + P(P) - P(P and B)

P(B or P) = 18/26 + 14/26 - 10/26

P(B or P) = 22/26 = 11/13