Worksheet: Tree Diagrams and Conditional Probability

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 1 3 2 4
  • B 1 6 9 5 7 6
  • C 1 2 2 3
  • D 1 3 4 6

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 5 3 3
  • B 2 1 1
  • C 1 3 1 6
  • D 5 3 2

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 4 1 5
  • B 1 4
  • C 1 2
  • D 8 1 5

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 1 4
  • B 3 5 1 4 4
  • C 3 5 7 2
  • D 1 2

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