Random experiments and sample space

Which of these experiments are random? Why?

1. a) Drawing a card from a well-shuffled pack and recording its suit.
2. b) Measuring the length of your notebook with a ruler.
3. c) Recording the number of goals in your team's next match.
4. d) Calculating the perimeter of a table given its dimensions.

State whether each of the following experiments is random or deterministic, justifying your answer:

1. a) Calculating the cost of $3$ kg of oranges at $2,10\ \text{€}$ per kilo.
2. b) Recording the outcome of dropping a drawing pin and seeing if it lands point up or on its side.
3. c) Measuring the time it takes for a litre of water to boil on the stove.
4. d) Recording who wins Saturday's basketball match.
5. e) Calculating the area of a square with a side length of $5$ cm.

Write down the sample space (all possible outcomes) for these experiments:

1. a) Rolling a die and recording the score.
2. b) Flipping a coin and recording the outcome.
3. c) Drawing a ball at random from a tombola drum with numbers from $1$ to $5$.

Write down the sample space for each of these random experiments:

1. a) Flipping a coin and recording the outcome.
2. b) Drawing a ball from an urn containing one red, one green, one blue and one yellow ball, and recording its colour.
3. c) Spinning a spinner with numbers from $1$ to $6$ and recording the number.
4. d) Choosing a day of the week at random and recording whether it is a "weekday" or "weekend".

When rolling a $6$-sided die, classify these events as certain, possible or impossible:

1. a) Rolling a $5$.
2. b) Rolling a $7$.
3. c) Rolling a number less than $7$.
4. d) Rolling a number greater than $2$.

In a box there are $6$ trading cards: $4$ of players and $2$ of team crests. If we pick a card at random, classify these events as certain, possible or impossible:

1. a) Picking a player card.
2. b) Picking a manager card.
3. c) Picking a player or team crest card.
4. d) Picking a team crest card.

We roll two dice of different colours (one blue and one green) and record the sum of the scores obtained.

1. a) How many different outcomes can the sum take? Write them all down.
2. b) Are these outcomes equally likely? Check this by completing a two-way table in your notebook showing the $36$ possible pairs (blue die, green die) and counting in how many ways each sum can be obtained.
3. c) Which sum is the most likely? How many ways are there to obtain it?
4. d) And which is the least likely?