2 ms·

I guess you're right. By my math, the probability of one given person knowing two answers out of four to win another R$ 1000 is way higher than the probability

I guess you're right. By my math, the probability of one given person knowing two answers out of four to win another R$ 1000 is way higher than the probability of four people answering exactly like the participant required to win the first R$ 1000. So it feels intuitive to take the final chance, specially given how much data/options the participant has (knows all the questions and correct answers already, and can choose any geek on the street). But I'm being purely rational - R$ 1000 on the hand is certainly worth more than a possible R$ 2000. Maybe if the final prize were R$ 10.000 or more people would chose differently?

derefr 14y ago
Also note: if the participant and their partners got all four questions wrong (but got them wrong together), the particpant still "wins", and moves on to the second round. But in this case, they have no evidence that the people on the street can be trusted to answer questions. If this scenario is common, it could be throwing off your expectations.
- hcarvalhoalves 14y ago
  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!
  - derefr 14y ago
    > assuming the knowledge of the population about trivial questions follows a normal distribution This is the assumption I question. Knowledge tends to cluster geographically--people in the same area get the same cable channels, on which are aired the same re-runs of Jeopardy on the same nights.

derefr 14y ago

Also note: if the participant and their partners got all four questions wrong (but got them wrong together), the particpant still "wins", and moves on to the second round. But in this case, they have no evidence that the people on the street can be trusted to answer questions. If this scenario is common, it could be throwing off your expectations.

hcarvalhoalves 14y ago
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!
- derefr 14y ago
  > assuming the knowledge of the population about trivial questions follows a normal distribution This is the assumption I question. Knowledge tends to cluster geographically--people in the same area get the same cable channels, on which are aired the same re-runs of Jeopardy on the same nights.