18. the picture shows nia’s coin collection. using the information from the picture, nia determined the…

Explanation:

Step1: Count total coins

There are 10 coins in total.

Step2: Analyze first statement

Coins worth more than $0.05$ are dimes, quarters. There are 4 such coins. Probability = $\frac{4}{10}=\frac{2}{5}$. So this statement is true.

Step3: Analyze second statement

Quarters and pennies: assume 3 quarters and 3 pennies (from visual - not given explicitly but for illustration). There are 6 such coins. Probability = $\frac{6}{10}=\frac{3}{5}$. So this statement is true.

Step4: Analyze third statement

Probability of choosing a nickel (assume 3 nickels), replacing it and then drawing a dime (assume 1 dime). Probability of nickel is $\frac{3}{10}$, probability of dime is $\frac{1}{10}$. Combined probability is $\frac{3}{10}\times\frac{1}{10}=\frac{3}{100}\neq\frac{3}{50}$. So this statement is false.

Step5: Analyze fourth statement

Probability of choosing two pennies without replacement. First penny probability is $\frac{3}{10}$, second penny probability is $\frac{2}{9}$. Combined probability is $\frac{3}{10}\times\frac{2}{9}=\frac{1}{15}\neq\frac{4}{25}$. So this statement is false.

Step6: Analyze fifth statement

Probability of choosing a dime (assume 1 dime), replacing it and then drawing a quarter (assume 3 quarters). Probability of dime is $\frac{1}{10}$, probability of quarter is $\frac{3}{10}$. Combined probability is $\frac{1}{10}\times\frac{3}{10}=\frac{3}{100}$. So this statement is true.

Step7: Analyze sixth statement

Nickel or dime: assume 3 nickels and 1 dime. There are 4 such coins. Probability = $\frac{4}{10}=\frac{2}{5}\neq\frac{4}{15}$. So this statement is false.

Answer:

• The probability of choosing a coin worth more than $0.05$ is $\frac{2}{5}$.
• The probability of choosing a quarter or a penny is $\frac{3}{5}$.
• The probability of choosing a dime, replacing it, then drawing a quarter is $\frac{3}{100}$.