In this worksheet, we will practice using tree diagrams to calculate conditional probabilities.
Q1:
A bag contains 13 white balls and 11 black balls. If 2 balls are drawn consecutively without replacement, what is the probability that both balls are white?
- A
- B
- C
- D
Q2:
A bag contains 27 white balls and 6 black balls. If 2 balls are drawn consecutively without replacement, what is the probability that the second ball is black given that the first is black?
- A
- B
- C
- D
Q3:
A bag contains 8 red balls and 8 black balls. If two balls are drawn without replacement, what is the probability of getting one red ball and one black ball?
- A
- B
- C
- D
Q4:
The probability that it rains on a given day is 0.6. If it rains, the probability that a group of friends plays football is 0.2. If it does NOT rain, the probability that they play football rises to 0.8.
Work out the probability that it rains on a given day and the friends play football.
Work out the probability that it does NOT rain on a given day and the friends play football.
What is the probability that the friends will play football on a given day?
Q5:
A bag contains a total of nine marbles: three are blue and six are red. Fady randomly takes a marble from the bag, records its color, and puts it back in. He then repeats this process. He draws the following tree diagram.
Write the values of the probabilities , , and in the probability tree. Give your answers as unsimplified fractions.
- A , ,
- B , ,
- C , ,
- D , ,
- E , ,
Use the probability tree to calculate the probability of choosing two blue marbles. Give your answer as a simplified fraction.
- A
- B
- C
- D
- E
Calculate the probability of choosing at least one red marble. Give your answer as a simplified fraction.
- A
- B
- C
- D
- E
Q6:
A bag contains 21 red balls and 15 black balls. If two balls are drawn without replacement, what is the probability of getting one red ball and one black ball?
- A
- B
- C
- D