Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Tree Diagrams and Conditional Probability

Q1:

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?

Q2:

A bag contains a total of nine marbles: three are blue and six are red. Michael 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 𝐴 , 𝐡 , and 𝐢 in the probability tree. Give your answers as unsimplified fractions.

  • A 𝐴 = 1 9 , 𝐡 = 1 9 , 𝐢 = 1 9
  • B 𝐴 = 3 9 , 𝐡 = 3 9 , 𝐢 = 3 9
  • C 𝐴 = 1 2 7 , 𝐡 = 1 2 7 , 𝐢 = 1 2 7
  • D 𝐴 = 6 9 , 𝐡 = 6 9 , 𝐢 = 6 9
  • E 𝐴 = 8 9 , 𝐡 = 8 9 , 𝐢 = 8 9

Use the probability tree to calculate the probability of choosing two blue marbles. Give your answer as a simplified fraction.

  • A 1 9
  • B 4 9
  • C 2 9
  • D 8 9
  • E 1 2 7

Calculate the probability of choosing at least one red marble. Give your answer as a simplified fraction.

  • A 2 3
  • B 4 9
  • C 8 9
  • D 5 9
  • E 1 9

Q3:

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

Q4:

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

Q5:

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

Q6:

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