8 A team called "The Educated Guess" enter a weekly quiz. If they win the quiz in a particular week, the probability that they will win the following week is 0.4 , but if they do not win, the probability that they will win the following week is 0.2 .
In week 4 The Educated Guess won the quiz.
- Calculate the probability that The Educated Guess will win the quiz in week 6.
Every week the same 20 quiz teams, each with 6 members, take part in a quiz. Every member of every team buys a raffle ticket. Five winning tickets are drawn randomly, without replacement. Alf, who is a member of one of the teams, takes part every week.
- Calculate the probability that, in a randomly chosen week, Alf wins a raffle prize.
- Find the smallest number of weeks after which it will be \(95 \%\) certain that Alf has won at least one raffle prize.