Monty Hall

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat.

What is the probability that the chosen door is open and you will see them in the car?

What is the probability that you change decision and open the remaining doors and see car?


Correct answer:

p1 =  33.3 %
p2 =  66.7 %
result if staying at door :  0 1

Step-by-step explanation:

behind door 1 behind door 2 behind door 3 result if staying at door #1 result if switching to the door offered
car goat goat car goat
goat car goat goat car
goat goat car goat car

p2=2/3 100=66.7%



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar




Tips to related online calculators
Would you like to compute count of combinations?

Related math problems and questions:

  • Scrap
    chair_bad From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
  • Logik game
    logik-game Letter game Logik is a two player game, which has the following rules: 1. The first player thinks five-letter word in which no letter is not repeated. 2. The second player writes a five-letter word. 3. The first player answers two numbers - the first numb
  • One three
    dice We throw two dice. What is the probability that max one three falls?
  • Three dice
    dices What is the probability that when we roll three dice, we roll the numbers 1,2,3?
  • Balls
    gulky From the bag with numbered balls (numbers 1,2,3,. ..20) we pick one ball. What is the probability of choosing a number containing 1?
  • Dices
    dices We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
  • Perfect cubes
    cubes3 Suppose a number is chosen at random from the set (0,1,2,3,. .. ,202). What is the probability that the number is a perfect cube?
  • Game 27
    dice Susan wanted to play the game. In the beginning, the first says a number from 1 to 8. Then the second player adds a number from 1 to 5 and tells the sum. Again, the Susan adds a number from 1-5 and say sum and etc. . . The winner must say the number 27. W
  • Cards
    cards Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probabi
  • Air draft
    numbers2 The numbers 1,2,3,4,5 are written on five tickets on the table. Air draft randomly shuffled the tickets and composed a 5-digit number from them. What is the probability that he passed: and, the largest possible number b, the smallest possible number c, a
  • Win in raffle
    tombola The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
  • Phone numbers
    old_phone How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
  • The test
    test The test contains four questions, and there are five different answers to each of them, of which only one is correct, the others are incorrect. What is the probability that a student who does not know the answer to any question will guess the right answer
  • Lock
    combination-lock A combination lock will open when the right choice of 3 numbers (from 1 to 16 inclusive) is selected. A. How many different lock combinations are possible? B. Is the combination lock named appropriately?
  • Three digits number
    plot How many are three-digit integers such that they no digit repeats?
  • Pediatrician
    doctor Pediatrician this month of 20 working days takes 8 days holidays. What is the probability that on Monday it will be at work?
  • Athletic club
    skola All athletic club boys lined up by size. In front of Peter was one-eighth of the total. Right behind Peter stood his brother Radek and behind Radek another five-sixths of the total number of boys. Mark the unknown total number of athletic club boys x. 1,