October 22, 2010

A Sigh of Relief

Wooo! Today, I got up in front of my class and delivered a mini math lesson on probability word problems! I have to say it was very scary to be up there and see 20 pairs of eyes looking back at you. It was even more nerve wrecking that one hour before it started but it went quite well with plenty of room for improvement. Basically what I did was give out two word problems, both of which were fairly difficult but doable. We did one problem together as a class and the other one I had them do in groups. Here were the two problems, try and see if you can solve them.

Problem 1: The Loaded Revolver

Henry has been caught stealing cattle, and is brought into town for justice. The judge is his ex-wife Gretchen, who wants to show him some sympathy, but the law clearly calls for two shots to be taken at Henry from close range. To make things a little better for Henry, Gretchen tells him she will place two bullets into a six-chambered revolver in successive order. She will spin the chamber, close it, and take one shot. If Henry is still alive, she will then either take another shot, or spin the chamber again before shooting.

Henry is a bit incredulous that his own ex-wife would carry out the punishment, and a bit sad that she was always such a rule follower. He steels himself as Gretchen loads the chambers, spins the revolver, and pulls the trigger. Whew! It was blank. Then Gretchen asks, "Do you want me to pull the trigger again, or should I spin the chamber a second time before pulling the trigger?" What should Henry choose?

Problem 2: The Monty Hall Paradox

Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. Would the contestant get a better deal if she switch or does switching not matter?

4 comments:

  1. haha...congrats on finishing your presentation!

    if i havent done my math wrong, i believe henry should NOT ask his wife to spin the chamber again...
    if she doesnt spin, the prob. that he will get shot becomes 1/4. if she spins again, the prob. is back to being 1/3, which is higher and thus less than desirable =p

    so...am i right? do i get a prize if i do? =)

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  2. BINGO! Right on the dot!

    prize? ummm...how about a lollipop? =D revive some childhood memories

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  3. Haha !!!

    I know the 2nd problem answer by watching "Las Vegas 21" a year ago ^^ it wasn't doors but cards instead ^^

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  4. HAHAHAHAAAA! the second one was pretty mind blowing once you know the answer and how they got to it. hahaha.

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