Brand new to statistics ,no strong math background please help.
Case 6.1
Suppose that you are a contestant on Lets make a deal. Monty has just given you a free trip touring toxic waste sites around the country. He now offers you a trade: Give up the trip in exchange for a gamble. On stage are three curtains, A, B, and C Behind one of them is a brand new car worth $20,000. Behind the other two curtains, the stage is empty. You decide to gamble and select Curtain A. In an attempt to make things more interesting, Monty then exposes an empty stage by opening curtain C (he knows here is nothing behind Curtain C). He then offers you a free trip again if you quit now or, If you like, propose another deal (i.e., you can keep your choice to curtain A or switch to Curtain B). What do you do? To answer the question, try first answering these questions.
1. Before Monty shows you what’s behind curtain C, What is the probability that the car is behind curtain A? What is the probability that the Car is behind curtain B?
2. After Monty shows you what’s behind Curtain C, what is the probability that the car is behind Curtain A? what is the probability that the car is behind Curtain B?
1. 1/3 and 1/3
2. 1/2 and 1/2
How much do you like toxic waste sites? Are there any fringe benefits to the trip?
To answer these questions, we can use a concept known as conditional probability. Conditional probability is the probability of an event occurring given that another event has already occurred.
1. Before Monty shows you what's behind curtain C:
- The probability that the car is behind curtain A is 1/3. This is because there are three curtains, and the car can only be behind one of them. So, each curtain has an equal chance of 1/3.
- Similarly, the probability that the car is behind curtain B is also 1/3.
2. After Monty shows you what's behind curtain C:
- Now, we have new information because Monty has revealed that there is nothing behind curtain C. This means that curtain C is no longer a possible option for where the car might be. So, we can eliminate it from consideration.
- This leaves us with two remaining curtains: A and B.
- The probability that the car is behind curtain A has not changed, as Monty's reveal did not provide any new information about curtain A. So, the probability that the car is behind curtain A remains 1/3.
- However, since we now know that curtain C is empty, the probability that the car is behind curtain B is now 2/3. This is because the car must be behind either curtain A or curtain B, and Monty's reveal narrows down the possibilities by eliminating curtain C.
So, after Monty shows you what's behind curtain C, it is actually more favorable for you to switch your choice to curtain B, as it now has a higher probability (2/3) of containing the car compared to curtain A (1/3).