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