Question 1: A bag contains 5 red, 3 blue, and 2 green balls. Two balls are drawn one after the other without replacement. What is the probability that both balls are red?

Answer: 0.28

Question 2: Construct a tree diagram for drawing two cards from a standard deck without replacement. Use the diagram to find the probability that both cards are aces.

Answer: 0.00495

Question 3: A box contains 4 defective and 6 non-defective lightbulbs. Three bulbs are tested without replacement. What is the probability exactly one defective bulb is found?

Answer: 0.432

Question 4: A student randomly picks two different books from a shelf of 8 books (4 fiction, 4 non-fiction) without replacement. What is the probability both are fiction?

Answer: 0.2857

Question 5: Using your constructed tree diagram, determine the probability that the second card drawn is an ace given that the first card was an ace.

Answer: 0.059

Question 6: A jar has 10 marbles: 4 red, 3 blue, and 3 yellow. Two marbles are drawn without replacement. What is the probability that at least one blue marble is drawn?

Answer: 0.55

Question 7: In a class of 12 students, 3 are selected at random without replacement to answer questions. What is the probability that the first student chosen is one of the top 4 students?

Answer: 1/4

Question 8: A bag contains 8 white, 5 black, and 7 brown balls. Two balls are drawn without replacement. Calculate the probability that one ball is white and the other is brown.

Answer: 0.366

Question 9: A deck of 52 cards is shuffled. Two cards are drawn without replacement. Use a tree diagram to find the probability that the first card is a king and the second is a queen.

Answer: 0.0072

Question 10: Identify a common mistake students make when calculating probabilities in without replacement scenarios and explain how to correct it.

Answer: Students sometimes multiply probabilities assuming independence. To correct this, they should update the probability after each draw based on the remaining items.