Independent and Dependent Events Practice Questions

Practice 2

Problems

1. One card is selected at random from a standard deck of 52 cards. The card is not 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, assuming that the first card chosen was not a red queen?
2. One card is selected at random from a standard deck of 52 cards. The card is not replaced, and then another card is selected. What is the probability that both cards selected are hearts?
3. 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, not replaced, and then another selected, what is the probability that the first tile is an A and the second another vowel?
4. At a picnic, a cooler contains 6 cans of apple juice and 4 cans of grape juice. Jerome selects a can of juice, drinks it, and then selects another can. What is the probability that both cans were apple juice?

Solutions

1. Read and understand the question. This question is looking for the probability of selecting a red card first, and a queen second. The events are dependent events because the first card is not replaced after it is selected.

Make a plan. Use the facts: there are 26 red cards and 4 queens in the deck, and there are a total of 52 cards. Because the first card is not replaced after it is chosen, the number of total possible outcomes decreases by one after the first card is selected. 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 solution is checking.

2. Read and understand the question. This question is looking for the probability of selecting a heart first, and another heart second. The events are dependent events because the first card is not replaced after it is selected.

Make a plan. Use the facts that there are 13 hearts in the deck, and there are a total of 52 cards. Because the first card is not replaced after it is chosen, the number of total possible outcomes decreases by one after the first card is selected. In addition, there will be one less heart in the deck. 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 another heart 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.

3. Read and understand the question. This question is looking for the probability of selecting an A and then another vowel when choosing two letter tiles at random. Because the first tile is not replaced, the events are dependent events.

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. If an A is selected first and not replaced, then there are only 4 vowels left and a total of 25 tiles. Find the probability of each situation and multiply them.

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

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

4. Read and understand the question. This question is looking for the probability that two cans of apple juice are selected at random from a cooler. Because the first can is not replaced, the events are dependent events.

Make a plan. Use the facts that there are 6 cans of apple juice and 4 cans of grape juice, for a total of 10 cans in the cooler. The first can of juice will not be replaced, so the number of cans of apple juice and the total number of cans will each decrease by one when selecting the second can.

Carry out the plan. The probability of selecting a can of apple juice for the first drink is . The probability that the second drink is also apple juice is . Multiply the probabilities: .

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