Q4) You are on a TV show and the presenter shows you 3 boxes: box 1, box 2 and, box 3. There is check for 1M $ in one of the boxes and if you guess the correct box you win 1M $ ! Let's assume you chose box 1. Now, assume you play the same game, but this time there are 1000 boxes, box 1, box 2, ..., box 1000. There is a check for 1M $ in one of the boxes and you have to guess the correct box to win the prize. Let's assume you chose box 1. d) What is the probability that the check is in box 1? e) What is the probability that the check is not in box 1? f) After you chose box 1, the presenter opens 998 boxes, other than box 1, and shows you that they are all empty. Now only box 1 and let's say box 349 are closed. Then, the presenter asks you if you want to change your initial decision and choose box 349 instead of box 1. Do you still choose box 1 or change your decision and choose box 349? Why?

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Q4) You are on a TV show and the presenter shows you 3 boxes: box 1, box 2 and, box 3.
There is check for 1M $ in one of the boxes and if you guess the correct box you win 1M $ !
Let's assume you chose box 1.
Now, assume you play the same game, but this time there are 1000 boxes, box 1, box 2, ..., box
1000. There is a check for 1M $ in one of the boxes and you have to guess the correct box to win
the prize.
Let's assume you chose box 1.
d) What is the probability that the check is in box 1?
e) What is the probability that the check is not in box 1?
f) After you chose box 1, the presenter opens 998 boxes, other than box 1, and shows you that
they are all empty. Now only box 1 and let's say box 349 are closed. Then, the presenter asks you
if you want to change your initial decision and choose box 349 instead of box 1. Do you still choose
box 1 or change your decision and choose box 349? Why?
Transcribed Image Text:Q4) You are on a TV show and the presenter shows you 3 boxes: box 1, box 2 and, box 3. There is check for 1M $ in one of the boxes and if you guess the correct box you win 1M $ ! Let's assume you chose box 1. Now, assume you play the same game, but this time there are 1000 boxes, box 1, box 2, ..., box 1000. There is a check for 1M $ in one of the boxes and you have to guess the correct box to win the prize. Let's assume you chose box 1. d) What is the probability that the check is in box 1? e) What is the probability that the check is not in box 1? f) After you chose box 1, the presenter opens 998 boxes, other than box 1, and shows you that they are all empty. Now only box 1 and let's say box 349 are closed. Then, the presenter asks you if you want to change your initial decision and choose box 349 instead of box 1. Do you still choose box 1 or change your decision and choose box 349? Why?
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