Not sure if my math is right, but cope with me... To win the first prize, four independent events should happen: the participant has to answer (either right or

Not sure if my math is right, but cope with me... To win the first prize, four independent events should happen: the participant has to answer (either right or wrong), and a random person in the street has to answer the same way. Let an event "QnPmAo" mean "Question n, Person m, Answer o", where n=4, and o can be 1 (right) or 0 (wrong). The probability of winning the first prize would be: P(Win) = (P(Q1P1A1 ∩ Q1P2A1) + P(Q1P1A0 ∩ Q1P2A0)) * (P(Q2P1A1 ∩ Q2P3A0) + P(Q2P1A1 ∩ Q1P3A0)) * ... and so on, for all four questions. To win the second prize, only two independent events are need: a participant knowing any two out of four questions. The probability would be: P(Win) = P(Q1 ∩ Q2) + P(Q2 ∩ Q3) + P(Q3 ∩ Q4) + P(Q1 ∩ Q4) From a statistical viewpoint, the second scenario seems always more likely than the first, assuming the knowledge of the population about trivial questions follows a normal distribution. If during the first round all four participants know the answers, the odds of a fifth participant knowing at least two are high. Still, from the episodes I watched, people seem to refuse the second challenge regardless of the outcome of the first round - in other words, they don't seem to make a rational decision. Hope someone less rough than me in statistics can shed some light if there's a mistake!