Calculating Basic Probabilities

A bag contains $\displaystyle 6$ red counters, $\displaystyle 4$ blue counters and $\displaystyle 5$ green counters.
One counter is chosen at random.
Calculate the probability that it is blue.

A bag contains $\displaystyle 6$ red counters, $\displaystyle 4$ blue counters and $\displaystyle 5$ green counters.
One counter is chosen at random.
Calculate the probability that it is not blue.

In a class of $\displaystyle 25$ pupils, $\displaystyle 14$ cycle to school.
One pupil is chosen at random.
Calculate the probability that the pupil does not cycle to school.

A fair six-sided die is rolled once.
State whether 'rolling a $\displaystyle 3$' and 'rolling an even number' are mutually exclusive. Justify your answer.

Two counters are taken from a bag, one after the other, and the first is not replaced.
State whether the two events are independent or dependent. Justify your answer.

A fair coin is flipped and a fair die is rolled.
State whether 'the coin lands on heads' and 'the die shows a $\displaystyle 6$' are independent. Justify your answer.

A student flips a fair coin and it lands on heads $\displaystyle 5$ times in a row.
The student says the next flip is more likely to be tails because tails is overdue.
Name the fallacy the student is using and explain why the student is wrong.

A spinner has $\displaystyle 8$ equal sections numbered $\displaystyle 1$ to $\displaystyle 8$.
Calculate the probability of spinning a number less than $\displaystyle 3$ or a number greater than $\displaystyle 6$.