The presenter of the game show 'Let's Make a Deal' is fed up with his work. He decides to steal the car (the prize of the show) and make off. He will be at the border and imprisoned. As punishment, he must do a variation each day with the jailer of the Monty Hall game, where neither the host nor the jailer know behind which of the three doors the car is hiding. After the first (random) choice of the guard, the presenter therefore chooses one of the two remaining doors at random and opens this one. In case he accidentally opens the door with the car, the jailer wins. If the host opens a door with a goat, then (as in the original Monty Hall game) the jailer chooses whether to stick with his original choice or leave the door to switch. At the end of the game, if the jailer opens a door with a goat, he must the game can be played again the next day, where the car is left behind again any door is blocked. The presenter may leave the cell as soon as the jailer the car won. (a) Assume the jailer is playing with the "don't switch doors" strategy. How big is the chance that the presenter will be released after ten days? And what are the chances that he spend at least ten days in jail? (b) The presenter convinces the jailer with a bribe of 1000 euros to go with the to play the "switch the door" strategy. Has the presenter spent his money well? if able please provide some explanation with the taken steps, thank you in advance
The presenter of the game show 'Let's Make a Deal' is fed up with his work. He
decides to steal the car (the prize of the show) and make off. He will be at the
border and imprisoned. As punishment, he must do a variation each day with the jailer
of the Monty Hall game, where neither the host nor the jailer know behind
which of the three doors the car is hiding. After the first (random) choice of the
guard, the presenter therefore chooses one of the two remaining doors at random and
opens this one. In case he accidentally opens the door with the car, the jailer wins.
If the host opens a door with a goat, then (as in the original Monty
Hall game) the jailer chooses whether to stick with his original choice or leave the door
to switch. At the end of the game, if the jailer opens a door with a goat, he must
the game can be played again the next day, where the car is left behind again
any door is blocked. The presenter may leave the cell as soon as the jailer
the car won.
(a) Assume the jailer is playing with the "don't switch doors" strategy. How big is
the chance that the presenter will be released after ten days? And what are the chances that he
spend at least ten days in jail?
(b) The presenter convinces the jailer with a bribe of 1000 euros to go with the
to play the "switch the door" strategy. Has the presenter spent his money well?
if able please provide some explanation with the taken steps, thank you in advance
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