In a game show, the host presents the player with three doors labeled 1, 2 and 3

Question

In a game show, the host presents the player with three doors labeled 1, 2 and 3. Behind two of the doors is a goat and behind the third is a new car. The contestant is asked to choose a door, winning what is behind the door, and let us suppose she chooses door 1. The host (who always knows which door hides the new car) then (truthfully) tells the contestant that there is a goat behind one of the doors that the contestant hasn't chosen, let us suppose door 2 in this case. The contestant is then allowed to change her door if she so chooses. The contestant thus has two strategies. A) Ignore the information that there is a goat behind door 2 and stick with door 1 B) Use the information that there is a goat behind door 2 to switch to door 3. (a) Which is the better strategy, A) or B) if the object is to choose the door hiding the car. (b) In a whole ensemble of games where the player opts for strategy A) what is the probability that the player wins the car. (c) In a whole ensemble of games where the player opts for strategy B) what is the probability that the player wins the car.

Explanation / Answer

(a) Both of the strategies have same probability of choosing car behind the door.

(b) If she opts for strategy A, The probability that she wins the game is 1/2

(c) If she opts for strategy B, The probability that she wins the game is again 1/2

Reason:-

Although she comes to know that their's a goat behind door 2 then also their are 2 doors left and the car can be behind anyone, 1 or 3. So their are still 2 options left making the probability of winning 1/2 for both the strategies.

If you do find this useful, please appreciate by giving a thumbs up

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.