Question
In: Advanced Math
Suppose you are on a game show and are shown three doors. Behind two are goats,...
Suppose you are on a game show and are shown three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, the host, who knows what's behind the doors, opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door (i.e., the door that neither you nor he opened). What should you do?
Solutions
Colby Messinger answered 2 years agoRelated Solutions
A game show has three doors for a contestant to choose from. Behind one of the...
A game show has three doors for a contestant to choose
from. Behind one of the doors is a brand new car, and behind the
other two doors are a goat. The contestant randomly
picks a door (⅓ probability of each). The host opens one of the
other two doors and reveals a goat. The host then gives the
contestant the option of keeping their original
door, or switching to the other unopened door. If the contestant
switches, what is...
1: You are on a game show standing in front of 3 doors. Behind 1 door...
1: You are on a game show standing in front of 3 doors. Behind 1
door there is a brand new car, behind the other 2 doors are goats.
You select door #2, but before the host opens your selected door,
he opens door #1, revealing a goat. The host then gives you the
option of changing your selection to door #3. Should you switch
doors? What is the probability that the car is behind door #3?
In the problem, you are on a game show, being asked to choose between three doors....
In
the problem, you are on a game show, being asked to choose between
three doors. Behind each door, there is either a car or a goat. You
choose a door. The host, Monty Hall, picks one of the other doors,
which he knows has a goat behind it, and opens it, showing you the
goat. (You know, by the rules of the game, that Monty will always
reveal a goat.) Monty then asks whether you would like to switch...
A game is played as follows. There are 2 goats and 1 car, each hidden behind...
A game is played as follows. There are 2 goats and 1 car, each
hidden behind a numbered door. You choose a door (for simplicity
you always choose door 1) and then Monty Hall opens one of doors 2
or 3.The door that he opens always reveals a goat. Now Monty offers
you to switch yourchoice of doors
(a) What is the probability that you win the car by switching
your choice? Hint: Consider the events {Ci= car is behind...
2. (Monty Hall) Suppose you are on a game show and are presented with three closed...
2. (Monty Hall) Suppose you are on a game show and are presented
with three closed doors
marked door 1, 2, and 3. Behind one door is a prize and behind the
other two are goats.
Suppose the host allows you to select one door, but the following
two rules apply:
• Before it is opened the host opens one of the two unselected
doors that has a goat behind
it.
• The host then allows you to switch your...
Using Rstudio # 1. Monty-Hall Three doors Recall the Monty-Hall game with three doors, discussed in...
Using Rstudio
# 1. Monty-Hall Three doors
Recall the Monty-Hall game with three doors, discussed in class.
Run a simulation to check that the probablility of winning
increases to 2/3 if we switch doors at step two.
Set up the experiment two functions "monty_3doors_noswitch" and
"monty_3doors_switch" (these functions will have no input
values):
```{r}
monty_3doors_noswitch <- function(){
}
monty_3doors_switch <- function(){
}
```
Use your two functions and the replicate function to compute the
empirical probablility of winning...
A game show has a host and three contestants. Suppose the three contestants are Meg, Tyler...
A game show has a host and three contestants. Suppose the three
contestants are Meg, Tyler and Ashley. The host and each contestant
each have a bag with 3 marbles; one red, one white and one blue.
The host will choose a marble from her bag, then Meg will choose a
marble from her bag. If Meg’s marble is the same color as the host,
then Meg has won and the game is over. If Meg loses, then Tyler
will...
(Monty Hall problem) Suppose you’re on a game show, and you’re given the choice of three...
(Monty Hall problem) Suppose you’re on a game show, and you’re
given the choice of three doors, say Door 1, Door 2, and Door 3.
Behind one door there is a car; behind the others, goats. Assume it
is equally likely that the car is behind any door, i.e., P(D1) =
P(D2) = P(D3). You will win whatever is behind the door you
choose.
(a) If you pick Door 1, what is your probability of winning the
car? [2 point]...
Suppose you are playing a dice game and you have three options to find a score....
Suppose you are playing a dice game and you have three options
to find a score. The options are:
A. Rolling an 11-sided die and using the outcome as your
score.*
B. Rolling two 4-sided dice, adding 1 to their sum, and using
that number as your score.
C. Rolling two 4-sided dice, doubling the result of the first
die and adding it to the result of the second, subtracting 1 from
this result, and using this number as your...
Suppose you are playing a dice game and you have three options to find a score....
Suppose you are playing a dice game and you have three
options to find a score. The options are:
Rolling an 11-sided die and using the outcome as your
score.*
Rolling two 4-sided dice, adding 1 to their sum, and
using that number as your score.
Rolling two 4-sided dice, doubling the result of the
first die and adding it to the result of the second, subtracting
1from this result, and using this number as your
score.
Assume that each...
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