Questions: Xavier's mother has a large collection of shoes. The table shows how many pairs of shoes she has in each style. flip-flops: 8 boots: 4 clogs: 6 If Xavier's mother chose a pair of shoes at random, what is the probability that the shoes would be flip-flops? Write your answer as a fraction or whole number.

$Xavier's mother has a large collection of shoes. The table shows how many pairs of shoes she has in each style. flip-flops: 8 boots: 4 clogs: 6 If Xavier's mother chose a pair of shoes at random, what is the probability that the shoes would be flip-flops? Write your answer as a fraction or whole number.$

Transcript text: Xavier's mother has a large collection of shoes. The table shows how many pairs of shoes she has in each style. \begin{tabular}{|l|c|} \hline flip-flops & 8 \\ \hline boots & 4 \\ \hline clogs & 6 \\ \hline \end{tabular} If Xavier's mother chose a pair of shoes at random, what is the probability that the shoes would be flip-flops? Write your answer as a fraction or whole number.

Solution

Solution Steps

To find the probability that Xavier's mother would choose flip-flops at random, we need to determine the ratio of the number of flip-flops to the total number of pairs of shoes. The probability is given by the formula:

\[ \text{Probability} = \frac{\text{Number of flip-flops}}{\text{Total number of pairs of shoes}} \]

Step 1: Determine the Total Number of Shoes

The total number of pairs of shoes is calculated as follows: \[ \text{Total} = \text{flip-flops} + \text{boots} + \text{clogs} = 8 + 4 + 6 = 18 \]

Step 2: Calculate the Probability of Choosing Flip-Flops

The probability $ P(\text{flip-flops}) $ is given by the ratio of the number of flip-flops to the total number of shoes: \[ P(\text{flip-flops}) = \frac{\text{Number of flip-flops}}{\text{Total number of shoes}} = \frac{8}{18} \]

Step 3: Simplify the Probability

The fraction $ \frac{8}{18} $ can be simplified: \[ P(\text{flip-flops}) = \frac{4}{9} \]