Any help, please? 13) Suppose you are on a game show, and you given the choice o

Question

Any help, please?

13) Suppose you are on a game show, and you given the choice of three doors. Behind one door is a Ferrari; behind the others two doors are bicycles. a) You pick a door, and the host, who knows what is behind the doors, opens another door, revealing a bicycle. He then says to you, "Do you want to pick the remaining unopened door instead of the door which you first picked?" Is it to your advantage to switch your choice? Justify your answer b) You pick a door, and the host, who (we know assume) does not know what is behind the doors, opens another door, revealing a bicycle. He then says to yoiu Do you want to pick the remaining unopened door instead of the door which you first picked?" Is it to your advantage to switch your choice? Justify your answer

Explanation / Answer

Given:

There are 3 doors and behind 1 door is ferrari and behind the other two are bicycles.

a) when we pick a door let's assume No.1 the probability of choosing 1 door out of 3 is, so we get probability = 1/3

As per given in question the host opens another door No.3 and revels that it has bicycle so if we choose another door No.2 then our probability of getting the same will increase because then we have to choose only from two doors rather then 3 so probability of getting the same will increase as 2/3 which is somewhat better then 1/3 .

b.) As same in answer a we have choosed the door No.1 and host revels another door No.3 who has bicycle so if we choose door No.3 with door No.1 then probability of getting the same would be increase from 1/3 to 2/3 which is somewhat better so this is our advantage because now we have to choose from 2 doors rather than 3 doors so it is quite easy for us to choose from 2 doors.and the winning chances will be quite high then last time.so as per question it is our advantage to switch the door.

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