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.