# 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 result:

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

#### Solution:

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

We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!

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

## Next similar math problems:

• 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
• The 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
• Scrap
From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
• Win in raffle
The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?
• PIN code
PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second d
• Probability of intersection
Three students have a probability of 0.7,0.5 and 0.4 to graduated from university respectively. What is the probability that at least one of them will be graduated?
• Perfect cubes
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?
• Table and chairs
Four people should sit at a table in front of a row of 7 chairs. What is the probability that there will be no empty chair between them if people choose their place completely at random?
• Freezer
The temperature is -8 degrees Celsius in the freezer. The outside temperature is 2 degrees Celsius. One minute took to change the temperature by one degree Celsius if we open the door. How many minutes the temperature in the freezer will rise?
• Bank
Paul put 10000 in the bank for 6 years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is 3.5%, and the tax on interest is 10%.
• 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
• Air draft
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
• One three
We throw two dice. What is the probability that max one three falls?
• Athletic club
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,
• Peaches
There are 20 peaches in the pocket. 3 peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten?
• Three dice
What is the probability that when we roll three dice, we roll the numbers 1,2,3?
• Three digits number
How many are three-digit integers such that in they no digit repeats?