High School

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1. A small restaurant sells coffee, tea, or fruit juice with a choice of a scone, chocolate cake, or meringue.

2.1 Draw a tree diagram that shows all the possible outcomes.

2.2 Calculate the probability that coffee and a scone will be ordered if we assume that people do not have any preference and can choose any combination.

2.3 If the order is taken at random, calculate the probability that tea and a scone or tea and a meringue is ordered.

2.4 If the restaurant has sold all the meringues and all the fruit juices, how many combinations are left?

Answer :

To solve these questions, we need to consider all the possible combinations of drinks and snacks. Let's go through this step by step.

2.1 Draw a tree diagram that shows all the possible outcomes:

For this problem, we'll list all combinations of drinks and snacks using a tree diagram structure, which outlines every possible pairing of the choices.

  1. First level - Drinks:

    • Coffee
    • Tea
    • Fruit Juice

  2. Second level - Snacks for each drink:

    • Scone
    • Chocolate Cake
    • Meringue

Thus, the tree diagram shows:

  • Coffee
    • Scone
    • Chocolate Cake
    • Meringue
  • Tea
    • Scone
    • Chocolate Cake
    • Meringue
  • Fruit Juice
    • Scone
    • Chocolate Cake
    • Meringue

There are a total of 9 possible outcomes (3 drinks * 3 snacks).

2.2 Calculate the probability that coffee and a scone will be ordered if we assume that people do not have any preference and can choose any combination:

There is exactly 1 combination that results in "coffee and a scone." Since there are 9 total combinations, the probability [tex]P[/tex] is:

[tex]P(\text{coffee and scone}) = \frac{1}{9}[/tex]

2.3 If the order is taken at random, calculate the probability that tea and a scone or tea and a meringue is ordered:

There are 2 combinations that satisfy this condition:

  1. Tea and a scone
  2. Tea and a meringue

Therefore, the probability [tex]P[/tex] is:

[tex]P(\text{tea and scone or tea and meringue}) = \frac{2}{9}[/tex]

2.4 If the restaurant has sold all the meringues and all the fruit juices, how many combinations are left?

Originally, we had 9 combinations. If all meringues (3 combinations) and all fruit juices (3 combinations) are no longer available, then:

Total remaining combinations = 9 - 3 (meringues) - 3 (fruit juices) = 3 combinations.

These remaining combinations would be:

  • Coffee and scone
  • Coffee and chocolate cake
  • Tea and chocolate cake

Therefore, 3 combinations are left.

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Rewritten by : Jeany

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