Y12 student and occasional WMC creator Noa claims that she can taste the difference between popular soft drinks Quiet Cake and Poppy Flax. I, however, doubt this and wish to test her claim, so I set up some experiments.

(1) I flip a coin; if it is heads, I pour a glass of QC, and if it is tails, I pour a glass of PF. Noa tastes it and guesses which brand it is. If she is correct, I flip another coin and pour another glass. I keep doing this until Noa gets one wrong.

How many would Noa need to get correct in a row before you were convinced that she could really taste the difference?

(2) I flip a coin ten times, and for each flip I pour a glass as above. Noa tastes all ten and guesses which brand each one is.

How many would Noa need to get correct to convince you that she can taste the difference?

(3) I pour four glasses of QC and four of PF, and arrange them in a random order. Noa tastes all eight and guesses which four are QC.

How many would Noa need to get correct to convince you that she can taste the difference?

(4) What other experiments can you think of to test Noa?