I don't know how to solve this question. For (a), some people say answer is 5/8, but I got 6/8, and I don't know which one is the correct answer! Please explain this monty hall problem for me!

Consider the following variation of the car-goat problem solved in class. This time there are four doors, with one car which is equally likely to be behind any of the four doors. The other three doors have goats behind them. You choose a door at random and then the host selects a door with a goat behind it at random, which he opens. Then, the hosts give you the option to switch your initial choice to one of the other two doors or to stick with your initial choice. (a) Suppose you now switch to one of the other two doors, picking one at random. What is the probability of winning the car? (b) What is the probability of winning the car if you don't switch? Hint: You can assume that the car is behind door 1 and follow the (I;H;F;R) notation used in class notes, where I is the initial door choice you make, H is the door host opens, F is the final door choice you make and R is the win (W) or lose (L) result.

Resources (2 door Monty Hall at page 10): https://drive.google.com/file/d/1SSEsL7iDN4J3v4JdaFq7DQzTaIb5GtaZ/view?usp=sharing

YouTube: https://www.youtube.com/watch?v=eyuKOWk_5Q4

P ( W )- P ( WA ) +P ( W, ) P (W ) + P (Up ) 5 +4 S Switch No switch 3 doors 2/3 Y 3 4 doon 5/9 #MontyHall #4doors #KumarShubham Monty Hall Problem | Build your Intuition with 3 and 4 door scenarios | Swi Download plained 785 views . Sep 9, 2021 1 22 DISLIKE SHARE DOWNLOAD & CLIP + SAVE . . .Possible onecomes = 4! = 4X3x2x! =24 outcomes ( 1 , 2 , 3, 4 ) , ( 1 , 2 , 4 , 3 ), (1, 3, 2, 4), ( 1 7 3, 4, 2), ( 1, 4, 2, 3), (4, 4, 3, 2) ( 2 , 1 2 8 x 4 ) , ( 2 , 1 / 4x 3 ) , ( 2 , 3 , 1 7 4 ) , ( 2, 3 , 4 , 1 ) , ( 2 , 4, 1, 3) , ( 2, 4 , 371 ) ( 3 , 1 2 8 5 4 ) , 1 3 , D # 5 2 ) , ( 3 , 2 , 1 , 4 ) , ( 3 , 2, 4 , 1), ( 3 , 4, 1, 2 ), 13, 4, 2, 1 ) ( 4 , 1x x x 3 ) , 1 4 , 1 2 X , 2 ) , ( 4 , 2 , 1 , 3 ) , ( 4 , 2, 3, 1), (4, 3 , 1,2 ), (4, 3, 2, 1 ) 24- 6= 18 possible outcomes equal probability of each outcom # et possible win outcome 6 9 x 3X /= 12 Thus ,6 18x6 -b 2 72 4 X z = 8 X 6 = 4 Is there a quicker way