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 sweatpants, given the size is small?\np(sweatpants | small) = ?% \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 sweatpants, given the size is small?\np(sweatpants | small) = ?% \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 two - way table, $P(\text{Sweatpants}|\text{Small})=\frac{\text{Number of small sweatpants}}{\text{Total number of small clothing items}}$.

Step2: Identify values from the table

The number of small sweatpants is 10, and the total number of small clothing items is 27.

Step3: Calculate the probability

$P(\text{Sweatpants}|\text{Small})=\frac{10}{27}\approx 0.3704$.

Step4: Convert to percentage

To convert the decimal to a percentage, multiply by 100: $0.3704\times100 = 37.04%$.

Step5: Round to the nearest whole percent

Rounding 37.04% to the nearest whole percent gives 37%.

Answer:

37%