Question
In: Statistics and Probability
Monty hall Problem Explain the statistical probabilities associated with the game show
Monty hall Problem
Explain the statistical probabilities associated with the game show
Solutions
orchestra answered 1 year agoRelated Solutions
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...
(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]...
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 variance of Monty Hall Problem. Let's say I am playing a game where there are...
A variance of Monty Hall Problem. Let's say I am playing a game
where there are 6 doors, there is a car behind 2 doors and there
are goats behind 4 doors. I don't know what is behind the doors but
I want a car. Let's say I pick a door at random, so Initially, my
chances of winning a car are 1/3. But before I open my door to see
if I won, the host of the game opens...
Suppose Monty Hall wants to make his game show more interesting. In the new version, there...
Suppose Monty Hall wants to make his game show more interesting.
In the new version, there are 7 doors and 2 cars behind the doors.
The other 5 doors have goats behind them. A contestant picks a
door. Monty Hall opens 3 of the doors with goats behind them (never
the door that the contestant picked or a door with a car). The
contestant then has the choice of switching doors.find the
probability that the contestant wins a car if...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall)...
consider the Monte Hall problem as discussed in lecture. Recall
that a game show host(Monte Hall) gives a contest a chance to
choose from three doors of which one is a new car and the other two
are goats. After the contestant chooses a door, the game show host
who knows what is behind all of the doors decides to open another
door behind which a goat sits. The games show host. then, offers
the contestant an opportunity to switch...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall)...
consider the Monte Hall problem as discussed in lecture. Recall
that a game show host(Monte Hall) gives a contest a chance to
choose from three doors of which one is a new car and the other two
are goats. After the contestant chooses a door, the game show host
who knows what is behind all of the doors decides to open another
door behind which a goat sits. The games show host. then, offers
the contestant an opportunity to switch...
consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall)...
consider the Monte Hall problem as discussed in lecture. Recall
that a game show host(Monte Hall) gives a contest a chance to
choose from three doors of which one is a new car and the other two
are goats. After the contestant chooses a door, the game show host
who knows what is behind all of the doors decides to open another
door behind which a goat sits. The games show host. then, offers
the contestant an opportunity to switch...
(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.
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