In a game show a contestant selects one of three doors:
- Behind one of the doors there is a prize and behind other two there is no prize.
- Each door has equal probability of having a prize.
- After contestant selects a door, the game show host who knows what's behind each of the doors, deliberately opens one of the remaining doors and reveals there is no prize behind it.
- The host then asks the contestant whether he want to $\text{SWITCH}$ his choice to other unopened door or $\text{STICK}$ to his original choice.
Which of the following options is/are correct ?:
$(1)$
Probability of winning the prize is same whether contestant $\text{STICK}$ or $\text{SWITCH}$
$(2)$
Probability of winning the prize when contestant $\text{STICK}$, is Image not present
$(3)$
Probability of winning the prize when contestant $\text{SWITCH}$, is Image not present
$(4)$
It is advantageous for contestant to $\text{SWITCH}$ than to $\text{STICK}$
The solution to this question is $(2)$, $(3)$, $(4)$
But according to me the solution should be only $(1)$ because the probability should be same for both the cases, either he $\text{SWITCHES}$ or $\text{STICKS}$ to his choice.
Can anyone explain.
