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#### 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?

b)  Classify the following experiments as random or determinist:

• I) Open the water tap.
• II) Toss a coin.
• III) Press the brake pedal of a car.
• IV) Draw a card from a deck of cards.

c)  Give two examples of random experiments.

d)  Give two examples of deterministic experiments.

e)  We draw a card from a deck of cards:

• I) What is the sure event?
• II) Give an example of an impossible event.

f)  In a pencil box there are 4 colour pencils: red, green, blue and yellow.

We take one pencil at random.

• I) What is the sample space?
• II) Name one elementary event.
• III) Name the event (event A) with the three non-elementary colours.

g)  In a pencil box there are 4 colour pencils: red, green, blue and yellow.

We take one pencil at random.

• I) Name one event (event A) with three colours. What is “not A”?
• II) What is the “sure event”?
• III) Name one “impossible event”.
• IV) Name another event (event B).
• V) Write A U B.
• VI) Write A ∩ B.

h)  In a pencil box there are 8 colour pencils: red, orange, yellow,

green, blue, purple, and violet.

We take one pencil at random.

• I) Write two events (A and B).
• II) Write “not A”.
• III) Write A U B.
• IV) Write A ∩ B.
• V) Write “not A” U B.
• VI) Write “not A” ∩ B.
• VII) Are A and B compatible? Why?
• VIII) Are A and B mutually exclusive? Why?

i)  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 results are: purple, yellow, blue, green, blue, red, blue, red, purple, and green.

• I)  What is the absolute frequency of colour red?
• II)  What is the relative frequency of colour red?
• III)  What is the absolute frequency of colour yellow?
• IV)  What is the relative frequency of colour yellow?
• V)  What is the absolute frequency of colour blue?
• VI)  What is the relative frequency of colour blue?

j)  In a football game a goal keeper stops 2 penalties from a total of 5 penalties.

• I)  What is the absolute frequency of stopping a penalty?
• II)  What is the relative frequency of stopping a penalty?

k)  Use Laplace’s Rule to calculate the probability of getting an even number when we roll a dice.