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 doors. For the purposes of this question, note the following:

1. The contestant initially selects door B

2.Game show host (Monte Hall) open door C behind which a goat sits

also note the following notation for events

1. Car A= the car is actually behind the door A

2. car B= the car is actually behind the door B

3. car C= the car is actually behind the door C

4. A= the host reveals a goat behind Door A

5.B=the host reveals a goat to be behind Door B

6.C= the host reveals a goat to be behind Door C

Given that the host reveals a goat behind Door C, what is the (conditional)probability that the car is actually behind door A [P(Car A| C)]?

Expert Solution

orchestra answered 2 years ago

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...

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...

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...

: Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company...

: Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company has 8 adjacent positions on its Boeing-727 aircraft for freight containers. The weights of this containers depend on what they are carrying. and company statistics indicate that %7 of the containers are classified as ”heavy”. While heavy containers are not inherently dangerous, having two such containers next to each other is considered dangerous should the plane encounter a wind gust. Understandably, company wants to...

Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company has...

Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company has 8 adjacent positions on its Boeing-727 aircraft for freight containers. The weights of this containers depend on what they are carrying. and company statistics indicate that %7 of the containers are classified as ”heavy”. While heavy containers are not inherently dangerous, having two such containers next to each other is considered dangerous should the plane encounter a wind gust. Understandably, company wants to know...

(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]...

Hotelling’s location game. Recall the voting game discussed in class. There are two candidates, each of...

Hotelling’s location game. Recall the voting game discussed in class. There are two candidates, each of whom chooses a position from the set S = (1,2,...10). The voters are equally distributed across these ten positions. Voters vote for the candidate whose position is closest to theirs. If the two candidates are equidistant from a given position, the voters at that position split their votes equally. First, unlike in the game analyzed in class, assume that both candidates only care about...

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...

Question

consider the Monte Hall problem as discussed in lecture. Recall that a game show host(Monte Hall)...

Solutions

Expert Solution

Related Solutions

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)...

Using Rstudio # 1. Monty-Hall Three doors Recall the Monty-Hall game with three doors, discussed in...

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...

: Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company...

Recall the airplane cargo problem we have discussed in our first lecture. An air-freight company has...

(Monty Hall problem) Suppose you’re on a game show, and you’re given the choice of three...

Hotelling’s location game. Recall the voting game discussed in class. There are two candidates, each of...

Recall the Monty Hall problem as presented in class. There are three caves, two of which...