**Mathematics 3** ESO – Unit 14 PROBABILITY page 125 activity 50

**a) **Watch the video on “Basic Probability” and answer:

- I) In mathematics, are things normally predictable or unpredictable? Why?
- II) What is the probability of an event?
- III) What means that an event has a probability of 1?
- IV) What is the probability of a “likely” event?
- V) What is the probability of rolling a 3 with a normal die? Why?
- VI) What is an outcome of a trial?
- VII) What do we have to do to get closer to the expected probability?
- VIII) What is the total probability if we add the probabilities of all possible outcomes of a trial? Why?
- IX) In a spinner with 16 sectors, what is the probability of getting a 5 or a 6? Why?

**2 –** Classify the following experiments as random or determinist:

- a) Open the water tap.
- b) Toss a coin.
- c) Press the brake pedal of a car.
- d) Draw a card from a deck of cards.

**3 –** Give two examples of random experiments.

**4 –** Give two examples of deterministic experiments.

**5 –** We draw a card from a deck of cards:

- a) What is the sure event?
- b) Give an example of an impossible event.

**6 –** In a pencil box there are 4 colour pencils: red, green, blue and yellow.

We take one pencil at random.

- a) What is the sample space?
- b) Name one elementary event.
- c) Name the event (event A) with the three non-elementary colours.

**7 –** In a pencil box there are 4 colour pencils: red, green, blue and yellow.

We take one pencil at random.

- a) Name one event (event A) with three colours. What is “not A”?
- b) What is the “sure event”?
- c) Name one “impossible event”.
- d) Name another event (event B).
- e) Write A U B.
- f) Write A ∩ B.

**8 –** In a pencil box there are 8 colour pencils: red, orange, yellow,

green, blue, purple, and violet.

We take one pencil at random.

- a) Write two events (A and B).
- b) Write “not A”.
- c) Write A U B.
- d) Write A ∩ B.
- e) Write “not A” U B.
- f) Write “not A” ∩ B.
- g) Are A and B compatible? Why?
- h) Are A and B mutually exclusive? Why?

**9 –** In a pencil box there are 6 colour pencils.

The experiment is to take one pencil at random (and put it back in the box). We repeat the experiment 10 times. The ten results are: purple, yellow, blue, green, blue, red, blue, red, purple, and green.

- a) What is the absolute frequency of colour red?
- b) What is the relative frequency of colour red?
- c) What is the absolute frequency of colour yellow?
- d) What is the relative frequency of colour yellow?
- e) What is the absolute frequency of colour blue?
- f) What is the relative frequency of colour blue?

**10 –** In a football game a goal keeper stops 2 penalties from a total

of 5 penalties.

- a) What is the absolute frequency of stopping a penalty?
- b) What is the relative frequency of stopping a penalty?

**11 –** Use Laplace’s Rule to calculate the probability of getting an

even number when we roll a dice.