Toán xác suất - Need help

Toán xác suất - Need help

In a far-away land, three prisoners?"Tom, Harry, and Dick?"are awaiting execution in separate cells. They have just heard the news that a healthy daughter has been born to the king and that the king has decided to express his gratitude to God by pardoning one of the prisoners. Because the monarch does not care which prisoner is spared, the lucky one has been chosen by lottery. Each prisoner has a 1/3 chance of being pardoned. The warden, who already knows the result of the lottery, has been instructed not to let any of the prisoners know if he is the one who will be pardoned. Arguing that everyone knows for sure that either Tom or Harry will be executed (because
only one or the other?"or neither?"of them will be spared), Dick persuadesthe warden that it would not be a violation of his instructions to tell Dick
whether Tom or Harry will be executed. The warden tells Dick that Harry
will be executed.
How does Dick feel?
a. No change: chance of survival is 1/3
b. Happy: chance of survival is 1/2
c. Ecstatic: chance of survival is 1
d. Unable to determine


Có bài này em nghĩ mãi ko ra giúp em với !!!!!

Theo những gì Dick biết được thì chỉ còn 2 khả năng có thể xảy ra: hoặc Dick hoặc Tom sẽ được tha. Và 2 khả năng này có xác suất ngang nhau, nên theo mình thì Dick sẽ vui vẻ nghĩ rằng xác suất hắn được tha là 1/2
kô biết đúng kô