8 Mark is playing solitaire on his computer. The probability that he wins a game is 0.2 , independently of all other games that he plays.
- Find the expected number of wins in 12 games.
- Find the probability that
(A) he wins exactly 2 out of the next 12 games that he plays,
(B) he wins at least 2 out of the next 12 games that he plays. - Mark's friend Ali also plays solitaire. Ali claims that he is better at winning games than Mark. In a random sample of 20 games played by Ali, he wins 7 of them. Write down suitable hypotheses for a test at the \(5 \%\) level to investigate whether Ali is correct. Give a reason for your choice of alternative hypothesis. Carry out the test.