Suppose you are on a game show and there are three closed doors. Behind one door is a car, and behind the other two doors are goats. Choose one door at random. What is the probability that you chose the winning door (the car)? Suppose that after you choose, but before your chosen door is opened, the host opens one of the unchosen doors, revealing a goat. The host then offers you the chance to change your choice to the remaining closed doors. What should you do? If you switch doors after one goat is revealed, does that increase, decrease, or have no effect on your chances? Why? What do you think the probability of winning is if you switch? If you don’t switch?

Suppose you are on a game show and there are three closed doors. Behind one door is a car, and behind the other two doors are goats. Choose one door at random. What is the probability that you chose the winning door (the car)? Suppose that after you choose, but before your chosen door is opened, the host opens one of the unchosen doors, revealing a goat. The host then offers you the chance to change your choice to the remaining closed doors. What should you do? If you switch doors after one goat is revealed, does that increase, decrease, or have no effect on your chances? Why? What do you think the probability of winning is if you switch? If you don’t switch?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

There are 40 pairs of shoes in Jaya's closet. They are all mixed up. If 20 shoes are picked, what is the chance that at most one shoe from each of the 40 pairs will be picked? (Remember, a left shoe is different than a right shoe.)
Jordan went to shelter to adopt a dog. There were 10 brown dogs and 10 black dogs. Jordan picked a dog, went home, then decided he wanted to go back and adopt another dog. What is the probability that he picked two black dogs?
Kiki has 7 black pens, 9 blue pens, and 6 red pens in her school bag.Kiki randomly picks two pens out of her school bag. What is the probability that Kiki chose two blue pens, if she replaced the first pen back in her pocket before choosing a second pen?
Suppose you are on a game show and there are three closed doors. Behind one door is a car, and behind the other two doors are goats. Choose one door at random. What is the probability that you chose the winning door (the car)?
Alice tosses a fair coin and throws a 6-sided die. Then, Bob tosses a fair coin and throws a 6-sided die too. If the sides they got for the coin flips are the same, Alice wins. If the sides they got for the coin flips are different, then whoever got the bigger number for their die roll wins. Otherwise, it's a tie. What is the probability of a tie?
There are two urns, one containing a blue sock and the other a red sock. A person randomly picks a sock. After this, someone puts a red sock in the empty urn. The person again randomly picks a sock and it is the probability that the first sock was red?
Milo will be having a sports camp next summer. 1 of the Coaches is Coach Mark and he will be handling basketball and volleyball clinics. He has 20 basketball balls and 15 volleyball balls. What is the probability that Coach Mark will get exactly 1 volleyball ball if Coach Mark take 4 balls at random?
Tom,Dick and Harry have three deck of cards.If each of them pick one card from their own deck at random,what is the probability that all three cards are Ace?
4. Let X and Y denote the lengths of life, in years of two components in an electronic system. If the joint density function of these variables is f(x, y) = fe-(x+y),x > 0,y >0 0, elsewhere. Find P(0 < X < 1|Y = 2)
Suppose you’re on a game show like Let’s Make A Deal and there are 4 doors to choose from. There are 3 mules and one car behind the four doors. Once you choose your door, the host will open one of the doors with a mule. This means that there are 3 unopened doors left, 2 with mules and 1 with the car. What is the probability of winning the car if you stick to your original choice? What is the probability if you switch to one of the other unopened doors? Explain your answer
Lebo had 3 blue pens, 2 red plens, 5 blue pens, and 2 pencils in her pencil case. What is the probability of taking a black pen and what is the probability of not taking a black pen?