a clothing store kept track of types and sizes of clothing sold over the period of one week. the two - way…

a clothing store kept track of types and sizes of clothing sold over the period of one week. the two - way table is given below:\n| | small | medium | large | total |\n|--|--|--|--|--|\n| t - shirt | 11 | 15 | 8 | 34 |\n| sweatshirt | 6 | 11 | 18 | 35 |\n| sweatpants | 10 | 14 | 7 | 31 |\n| total | 27 | 40 | 33 | 100 |\nwhat is the probability that a randomly selected clothing item from this table is medium, given it is a sweatshirt?\np(medium | sweatshirt) = ?%\nround your answer to the nearest whole percent.

a clothing store kept track of types and sizes of clothing sold over the period of one week. the two - way table is given below:\n| | small | medium | large | total |\n|--|--|--|--|--|\n| t - shirt | 11 | 15 | 8 | 34 |\n| sweatshirt | 6 | 11 | 18 | 35 |\n| sweatpants | 10 | 14 | 7 | 31 |\n| total | 27 | 40 | 33 | 100 |\nwhat is the probability that a randomly selected clothing item from this table is medium, given it is a sweatshirt?\np(medium | sweatshirt) = ?%\nround your answer to the nearest whole percent.

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of the table, $P(\text{Medium}|\text{Sweatshirt})=\frac{\text{Number of medium sweatshirts}}{\text{Total number of sweatshirts}}$.

Step2: Identify values from the table

The number of medium sweatshirts is 11, and the total number of sweatshirts is 35.

Step3: Calculate the probability

$P(\text{Medium}|\text{Sweatshirt})=\frac{11}{35}\approx 0.3143$.

Step4: Convert to percentage

To convert the decimal to a percentage, multiply by 100: $0.3143\times100 = 31.43%$.

Step5: Round to the nearest whole - percent

Rounding 31.43% to the nearest whole - percent gives 31%.

Answer:

31%