5. Six standard dice with faces numbered 1 to 6 are thrown together.
Assuming that the dice are fair, find the probability that
- none of the dice show a score of 6,
- more than one of the dice shows a score of 6,
- there are equal numbers of odd and even scores showing on the dice.
One of the dice is suspected of being biased such that it shows a score of 6 more often than the other numbers. This die is thrown eight times and gives a score of 6 three times.
- Stating your hypotheses clearly, test at the \(5 \%\) level of significance whether or not this die is biased towards scoring a 6.
(7 marks)