Statistics

State whether the two events are dependent or independent. Justify your reasoning.

1. Selecting an ace from a standard deck of cards, replacing it, and then selecting a jack from the deck.

2. A numbered ball between 1 and 100 is selected from a bucket, and then a second numbered ball is selected from the remaining balls.

Calculate the following probabilities. Don’t forget to include work.

3. What is the probability of flipping a coin 8 times in a row and getting heads every time?

4. Given a standard deck of cards, what is the probability of selecting a diamond, replacing it, selecting a queen, replacing it, and then selecting a spade?

5. Given a standard deck of cards, what is the probability of selecting the queen of hearts and then any heart, without replacing the queen of hearts?

In a box of 11 parts, four of the parts are defective. Two parts are selected at random, without replacement.

6. Find the probability that both of the parts are defective.

7. Find the probability that both of the parts are not defective.

8. Find the probability that at least one of the two parts is defective.