Question

sample response:no. choosing two dimes are dependent events. the probability of choosing the first dime is $\frac{1}{4}$ and the probability of choosing the second dime is $\frac{1}{7}$. the probability that both coins are dimes check all that you considered in your response. the events are dependent. the size of the original sample space is 8. it changes to 7 after the first dime is chosen. the probability of picking the first dime is 2/8. the probability of picking the second dime is 1/7 to find the probability of the compound event, multiply the probabilities.

Explanation:

Step1: Identify event - dependence

The events are dependent as the outcome of the first coin - pick affects the second.

Step2: Determine first - pick probability

If there are 2 dimes out of 8 coins initially, the probability of picking the first dime is $\frac{2}{8}$.

Step3: Determine second - pick probability

After picking one dime, there is 1 dime left out of 7 coins, so the probability of picking the second dime is $\frac{1}{7}$.

Step4: Calculate compound - event probability

For dependent events, we multiply the probabilities of each event to find the probability of the compound event.

Answer:

The events are dependent. The size of the original sample space is 8. It changes to 7 after the first dime is chosen. The probability of picking the first dime is 2/8. The probability of picking the second dime is 1/7. To find the probability of the compound event, multiply the probabilities.