He cheats! A friend of yours claims that when he tosses a coin he can control the outcome. You are skeptical and want him to prove it. He tosses the coin, and you call heads; it’s tails. You try again...

He cheats! A friend of yours claims that when he tosses a coin he can control the outcome. You are skeptical and want him to prove it. He tosses the coin, and you call heads; it’s tails. You try again and lose again.

a) Do two losses in a row convince you that he really can control the toss? Explain.

b) You try a third time, and again you lose. What’s the probability of losing three tosses in a row if the process is fair?

c) Would three losses in a row convince you that your friend cheats? Explain.

d) How many times in a row would you have to lose in order to be pretty sure that this friend really can control the toss? Justify your answer by calculating a probability and explaining what it means.