Visit the web site: http://math.edu/crypto/Monty/monty.html Play 20 games and do NOT switch door. Record your wins/losses and how many times the nice...

Visit the web site: http://math.ucsd.edu/∼crypto/Monty/monty.html Play 20 games and do NOT switch door. Record your wins/losses and how many times the nice prize was behind the first selected door. Then play 20 games and switch door every time. Record your wins/losses and how many times the nice prize was behind the first selected door.

With NO Switch I had 6 Wins, 14 Losses, 5 Car behind the first selected door, and 30 % wins.

With Switches I had 9 Wins, 11 Losses, 11 Car behind the first selected door, and 45 % wins.

(a) Based on the combination of your two simulations, what is the probability that you would have picked the nice prize on the first selection?

(b) Based on the combination of your two simulations, which is better, to stay or switch? Why?

(c) Intuition suggests that it shouldn't matter whether you stay or switch, the P(nice prize) is still 1/3, right? Do you agree or disagree? Why?

(d) Consider the following tree diagram. Use it to calculate the P(each outcome). Fill in the four blanks with probabilities.

(e) Regardless of what you originally choose, what is P(car) if you stay? Show work.

(f) Regardless of what you originally choose, what is P(car) if you switch? Show work. (h) Base on (f) and (g), is it better to switch or stay? Why?