Sign in to jmaths to print this page or save it as a PDF: jmaths-8ce638778fd6.herokuapp.com/maths/ai-hl/probability/13-1-3/problems/b/

jmaths

IB Mathematics: Applications and Interpretation HL · 13.1: Probability · 13.1.3

Name Date

Tree diagrams and sample spaces Problem set B

Draw a tree diagram, a Venn diagram or a sample space diagram. Multiply along branches and add the end outcomes you want. Give a probability as a fraction in lowest terms, or as a decimal when the numbers are decimals.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. Tomorrow it will rain with probability 0.35. If it rains, the probability that Omar takes the bus is 0.8. If it does not rain, the probability that he takes the bus is 0.3. Find the probability that

    1. (a) it rains and Omar takes the bus.
    2. (b) Omar takes the bus.

  2. A box contains 5 black cubes and 4 white cubes. Two cubes are taken at random, one after the other, without replacement. Find the probability that

    1. (a) both are black.
    2. (b) the two are different colours.

  3. The Venn diagram shows probabilities for the people at a leisure centre. C is the event "uses the café" and B is the event "books a class". A person is chosen at random.

    0.410.290.12xCB
    1. (a) Find the value of x.
    2. (b) Find the probability that the person uses the café.
    3. (c) Find the probability that the person books a class but does not use the café.

  4. Two fair five-sided spinners, each numbered 1 to 5, are spun and the scores are added. Draw a sample space diagram and find the probability that

    1. (a) the sum is 7
    2. (b) the sum is less than 4

  5. A family has two children. Each child is equally likely to be a boy (B) or a girl (G). Find the probability that the family has

    1. (a) exactly one girl.
    2. (b) at least one boy.

  6. Three tiles show the letters K, I and T. They are placed in a row in a random order. List all the arrangements and find the probability that the last letter is a vowel.

  7. A jar holds 2 mint sweets and 7 toffee sweets. A sweet is taken at random, its type is noted and it is put back. A second sweet is then taken. Find the probability that

    2/9M2/9M4/817/9T14/817/9T2/9M14/817/9T49/81
    1. (a) both sweets are mint.
    2. (b) the two sweets are different types.

In context

  1. A bakery makes 65% white loaves and the rest brown. 4% of the white loaves and 9% of the brown loaves are returned by customers. A loaf is chosen at random. Find the probability that it

    1. (a) is white and is returned.
    2. (b) is returned.

  2. A tin holds 4 blue, 3 black and 2 red pens. Two pens are taken at random without replacement. Find the probability that both are the same colour.

  3. A seed company says that each seed it sells grows with probability 0.6, independently. A gardener plants three seeds. Find the probability that

    1. (a) exactly two seeds grow.
    2. (b) at least one seed grows.

Stretch

  1. A tray holds 8 eggs, 3 of which are cracked. Two eggs are taken without replacement. Find the probability that at least one is cracked.

  2. A fair four-sided die and a fair five-sided spinner are rolled and the scores are added. Find the probability that the sum is a multiple of 3.

jmaths.xyz · AI HL · 13.1.3 Tree diagrams and sample spaces