Problem 1 A fair coin is tossed six times. We want to compute: a) the probability of finding at least four heads within all the six tosses (no matter where) b) If Bob accepts a bet of 10 Euros and...

Extracted text: Problem 1 A fair coin is tossed six times. We want to compute: a) the probability of finding at least four heads within all the six tosses (no matter where) b) If Bob accepts a bet of 10 Euros and pays 50 Euros in case of a sequence of exactly four consecutive heads appearing within the six tosses, which is the average gain of Bob for each bet? c) If an unfair coin with p = P[H] =1/4 is used instead of the fair one, how does the gain in point b) change?