R Tutorial: Monty Hall

Key Takeaways

another well-known probability puzzle is Monty Hall which is named after the host of a game show called let's make a deal in this puzzle a contestant is shown three doors behind one of the doors is a prize and the other doors contain no prize historically the prize was a car and the non prizes were goats the game begins with the contestant picking a door supposed that the contestant has chosen door number one the host Monty Hall then opens one of the other doors that does not contain the price the contestant has a choice to stick or switch to stick means to stay with the original choice here door number one and two switch means to choose the remaining door here door number three which strategy gives the greatest probability of winning the prize and what are the probabilities with each strategy a common misconception is that sticking or switching both give a 50/50 chance of winning since there are only two remaining doors in this puzzle we will write code to simulate both strategies to demonstrate the true win probability in each case to solve this problem we need to handle some art indexing specifically when determining which door the host should reveal consider the doors object which contains the values 1 2 & 3 to represent each door if the contestant chooses door number 1 and the prize is behind door number 2 then the only possible door that the host can reveal is door number 3 from a coding standpoint we must exclude doors 1 and 2 from the possibilities of doors to reveal we can do this by using a minus index with the C concatenate er to remove doors 1 & 2 as possibilities then the value of the reveal is only door number 3 note that in general we can reference elements of the doors object by supplying either an explicit numeric index or a variable name here we knew that door number one was the choice and door number two contained the prize so we could supply the numbers one and two in the reverse indexing in our exercises the prize door will be chosen randomly so it must be coded by a variable name that contains the value of the prize door rather than simply with number two as it was here in the previous slide the initial choice and the prize door were different leaving only one remaining door for the host to reveal since the host will only reveal a door with no price if the initial choice is the same as the prize door then there are two possible doors for the host to reveal in this case it must be random which can be done using the sample function what we want to sample is the doors object with the initial choice removed from it using the negative indexing strategy from the previous slide here the prize and initial choice were door number one but if it were random we would have to assign it a variable name and then access it using that name let's use these concepts to simulate our solution to the month