Tom...a math problem for you

[MattK]

Tom- I'm fairly certain that you've heard of this one but was curious as to what you think about it...

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors?

It reminds me a lot of the game show "Let's make a Deal". What would be the best thing to do...switch or stay with your original case knowing 1 case has a million and the other a dollar?

 

[Tom]

Yeah, I heard of this, let me see if I can refigure it.

My first choice, I had 1/3 chance of getting the car.

Even if I picked a goat, there is still a goat door to open for the host, like he did.

So, now, I have a goat and a car door.

Prob.1/2 one is the car, 1/2 its another goat, but wait.

Was the first door opened a trophy goat?

I'll label the doors C for car, G1 for goat 1, G2 for goat 2.

Here's the three possibilities of my 1st choice.

If I picked C, he could pick a goat door and I should not switch.

If I picked G1, he opened G2, and I should switch.

If I picked G2, he would open G1, and I should switch.

2 out of 3 of my choices indicate I should switch.

I think I should switch, if I want the car and not the goat. It would be advantagious (sp?) to switch, if you want the car.

Is that right?

 

[MattK]

Tom- From what I understand, that's correct. At first, I thought 50-50 but when the probabilities were tested, indeed you are much more likely to win a car by switching. Here are a couple more...What do you think?

A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're male, female, or a pair. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. "Is at least one a male?" she asks him. "Yes!" she informs you with a smile. What is the probability that the other one is a male?

Say that a woman and a man (who are unrelated) each has two children. We know that at least one of the woman's children is a boy and that the man's oldest child is a boy. Can you explain why the chances that the woman has two boys do not equal the chances that the man has two boys? My algebra teacher insists that the probability is greater that the man has two boys, but I think the chances may be the same. What do you think?