Bonus Problem: Congratulations! Once again you are a contestant on a game show.

Question

Bonus Problem: Congratulations! Once again you are a contestant on a game show. This time, the host shows you 5 curtains. He tells you that behind 3 of the curtains lie a farm animal, and behind the other 2 curtains lie a private jet (and two charter pilots that will fly your private jet with that). He then asks you to choose 2 curtains. If these 2 curtains are the ones with the 2 private jets behind them, then you will win those private jets. Else you will go home with nothing. After you choose your 2 curtains, the host opens one of the remaining three curtains that he knows has a farm animal behind it. He then gives you the following options (0) stick with the curtains you initially chose, (1) swap either one of your curtains for one of the remaining curtains, or (2) swap both of your curtains for the remaining 2 curtains. Let pli), where i 0, 1, 2, be the respective probabilities of winning the money in scenarios () as outlined above. Find: P(O), P(1), and P(2).

Explanation / Answer

Given that the host has opened one curtain which has a farm animal

Now there are 4 curtains in total out of which we have choosen 2

P(0)=When we stick with our options ie we choose 2 curtains out of the remaining 4

P(0)=2/4=1/2=0.50

P(1)= We can swap 1 curtain with the remaining curains

Here we are fixed with 1 curtain so we can choose from the remaining 3 curtains

Hence P(1)=1/3=0.33

P(2)=Swap both curtains with other 2

This brings us to the similar problem as P(0)

We need to choose 2 curtains from 4 curtains

P(2)=2/4=1/2=0.50

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