Question
In: Statistics and Probability
Recall the Monty Hall problem as presented in class. There are three caves, two of which...
Recall the Monty Hall problem as presented in class. There are three caves, two of which contain dragons and one of which is a hiding princess. The prince chooses a cave and a wizard (truthfully) reveals to the prince that one of the other caves has a dragon. 2 The prince now has the option to switch to the other cave (the one he didn’t choose and wasn’t revealed to have a dragon), and try his luck finding the princess in that cave instead. (a) Explain why the prince should always switch caves. (b) Now suppose there are four caves, three of which contain a dragon and one of which contain a princess. After the prince makes his first choice, the wizard reveals two of the caves with dragons (separate from the one the prince chose originally). Should the prince stay or switch? Are the probabilities different than (a)?
Solutions
orchestra answered 1 year agoRelated Solutions
Recall the Monty Hall problem as presented in class. There are three caves, two of which...
Recall the Monty Hall problem as presented in class. There are
three caves, two of which contain dragons and one of which is a
hiding princess. The prince chooses a cave and a wizard
(truthfully) reveals to the prince that one of the other caves has
a dragon. 2 The prince now has the option to switch to the other
cave (the one he didn’t choose and wasn’t revealed to have a
dragon), and try his luck finding the princess...
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...
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...
(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]...
(a) In the Monty Hall problem with 100 doors, you pick one and Monty opens 98...
(a) In the Monty Hall problem with 100 doors, you pick one and
Monty opens 98 other doors with goats. What is the probability of
winning (assuming you would rather have a car than a goat) if you
switch to the remaining door? Explain your answer.
(b) Suppose Monte opens 98 doors without checking for cars. What is
the probability that, once the doors are open, changing your choice
will not change your chances of winning.
There are three caves, two of which contain dragons and one of which is a hiding...
There are three caves, two of which contain dragons and one of
which is a hiding princess. The prince chooses a cave and a wizard
(truthfully) reveals to the prince that one of the other caves has
a dragon. 2 The prince now has the option to switch to the other
cave (the one he didn’t choose and wasn’t revealed to have a
dragon), and try his luck finding the princess in that cave
instead. (a) Explain why the prince...
1. (a) Consider a modified version of the Monty Hall problem. In this version, there are...
1. (a) Consider a modified version of the Monty Hall problem. In
this version, there are 8 boxes, of which 1 box contains the prize
and the other 7 boxes are empty. You select one box at first.
Monty, who knows where the prize is, then opens 6 of the remaining
7 boxes, all of which are shown to be empty. If Monty has a choice
of which boxes to open (i.e. if the prize is in the box you...
1. (a) Consider a modified version of the Monty Hall problem. In this version, there are...
1. (a) Consider a modified version of the Monty Hall problem. In
this version, there are 8 boxes, of which 1 box contains the prize
and the other 7 boxes are empty. You select one box at first.
Monty, who knows where the prize is, then opens 6 of the remaining
7 boxes, all of which are shown to be empty. If Monty has a choice
of which boxes to open (i.e. if the prize is in the box you...
Monty hall Problem Explain the statistical probabilities associated with the game show
Monty hall Problem
Explain the statistical probabilities associated with the game
show
The Monty Hall problem is a famous problem loosely based on the game show Let's Make...
The Monty Hall problem is a famous problem loosely based on the
game show Let's Make a Deal. You are a contestant on the game show.
There are 3 doors in front of you. Behind one door is a prize, and
behind the other two doors are goats. Assume the door with the
prize is picked uniformly at random from the three doors.
First, you pick a door. Then, Monty Hall will open one of the
other two doors that...
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