Sunday Times Teaser 3148 – Quiz Probabilities
by Edmund Marshall
Published Sunday January 22 2023 (link)
Each of four contending couples in a quiz game has equal probability of elimination at the end of each of the first three rounds, one couple going after each round. In the fourth round, the remaining couple has a constant probability p, less than ½, of winning the jackpot, which consists of £1000 in the first game; if the jackpot is not won, it is added to the £1000 donated in the next game. Each couple may enter three successive games of the quiz, except that any couple having played for the jackpot in the fourth round of any game then withdraws altogether, being replaced by a new couple in the next game.
If the probability that a couple, competing from the first game, wins £2000 is 7/96, what is the value of p as a fraction?