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# Independent and Dependent Events Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to Independent and Dependent Events Study Guide.

## Independent and Dependent Events Practice Questions

### Practice 1

#### Problems

1. One card is selected at random from a standard deck of 52 cards. The card is replaced, and then another card is selected. What is the probability that the first card chosen is a red card and the second card chosen is a queen?
2. One card is selected at random from a standard deck of 52 cards. The card is replaced, and then another card is selected. What is the probability that the first card chosen is a heart and the second card chosen is a diamond?
3. A red die and a white die are each rolled while playing a board game. What is the probability of getting a 1 on the red die and a 4 on the white die?
4. A game uses 26 letter tiles. Each tile has one letter on it and each letter of the alphabet appears once on the tiles. If one tile is selected at random, replaced, and then another selected, what is the probability that the first tile is an A and the second another vowel?

#### Solutions

1. Read and understand the question. This question is looking for the probability of selecting a red card first, and then a queen second. The events are independent events because the first card is replaced after it is selected.
2. Make a plan. Use the facts that there are 26 red cards and 4 queens in the deck, and there are a total of 52 cards. Because the first card is replaced after it is chosen, the number of total possible outcomes is always the same (52). Find the probability of each event and multiply them.

Carry out the plan. The probability of first selecting a red card at random is . The probability of selecting a queen second is . Multiply these probabilities to find the probability that both events will happen: .

Check your answer. To check this solution, multiply the probabilities again. Because , this answer is checking.

3. Read and understand the question. This question is looking for the probability of selecting a heart first, and a diamond second. The events are independent events because the first card is replaced after it is selected.
4. Make a plan. Use the facts that there are 13 hearts and 13 diamonds in the deck, and there are a total of 52 cards. Because the first card is replaced after it is chosen, the number of total possible outcomes is always the same (52). Find the probability of each event and multiply them.

Carry out the plan. The probability of first selecting a heart at random is. The probability of selecting a diamond second is . Multiply these probabilities to find the probability that both events will happen: .

Check your answer. To check this solution, multiply the probabilities again. Because , this solution is checking.

5. Read and understand the question. This question is looking for the probability of rolling a 1 on the red die and a 4 on the white die. The events are independent events because the outcome of one die does not depend on the outcome of the other.
6. Make a plan. Use the facts that there are 6 sides to a die, and one side has 1 dot and one side has 4 dots. Find the probabilities for each event and multiply them.

Carry out the plan. The probability of rolling a 1 on the red die is , and the probability of rolling a 4 on the white die is also . Multiply these to find the total probability: .

Check your answer. To check this solution, multiply the probabilities again. Because , this solution is checking.

7. Read and understand the question. This question is looking for the probability of selecting an A and another vowel when choosing two letter tiles at random. Because the first tile is replaced, the events are independent events.
8. Make a plan. Use the fact that there are 26 different tiles, each with a different letter. There is one tile with an A and 5 tiles in total with vowels. Find the probability of each situation and multiply them together.

Carry out the plan. The probability of selecting an A is and the probability of selecting a vowel is . The probability of both events happening is .

Check your answer. To check this solution, multiply the probabilities together again. Because , this solution is checking.

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