Please answer as soon as possible 4. Consider the Monty Hall problem from Stage
ID: 3042509 • Letter: P
Question
Please answer as soon as possible 4. Consider the Monty Hall problem from Stage 1 of this lab, but where instead we have 5 doors, only one of which conceals a fabulous prize behind it (the others have goats behind them). The contestant picks an initial door that she thinks contains the fabulous prize. The host is then required to open 2 doors, both of which will have goats behind them. The contestant is then offered the choice to switch to one of the two remaining unopened doors. What is the probability that the contestant will win if she chooses to switch doors? What is the probability that the contestant will win if she does not switch doors? a) b) Should the contestant switch to one of the other doors?
Explanation / Answer
When there are five doors and one has a prize, the probability of picking he prize is 1/5.
a)
2 doors are now opened and then the contestant is left with 1 door (containing the prize) and 2 doors (containing the goats)
therefore the probability of switching doors mean, the probability of picking the prize has gone up to 1/3.
If she has not switched, the probabilty of winning the prize remains the same i.e. 1/5.
b)
yes she should switch to one of the other two doors, as the probability will be 1/3 to win a prize.