Plato: Good morning, class, today's lesson is on probability.
Aristotle: Fantastic.
I'm headed to Vegas this weekend, and I can use some pointers.
P: Curb your enthusiasm kid, this is serious stuff.
Here, roll this pair of dice, but don't look at the the result. OK, good.
Now without looking, tell me the probability that you rolled a seven.
If you're going to play craps this is important.
By the way, I can tell you that one of your dice is a four.
A: Hmm...
So I could have rolled 41 42 43 44 45 46 14 24 34 54 or 64,
all with equal likelihood, with 34 and 43 making seven.
That's a probability of 2/11.
P: You're on a roll kid, now let's do it again. Great.
Again without looking, what's the probability you rolled a seven?
By the way, I can tell you one of your dice is a one.
A: So I could have rolled 11 12 13 14 15 16 61 51 41 31 or 21,
with 16 and 61 making seven. Hmm... it's the same as before - 2/11.
P: And if I had told you one of your dice was a five?
A: Well ... I guess it really doesn't matter what number you tell me. It will always come out the same. The probability will be 2/11.
P: So what can we deduce from that?
A: That the probability of two dice making seven is ... 2/11.
But wait... Hey, you're not really Professor Plato, are you?
P: No. I'm an insurance salesman.
So ... what exactly is the probability of making seven?
Plato: Good morning, class, today's lesson is on probability.
Aristotle: Fantastic.
I'm headed to Vegas this weekend, and I can use some pointers.
P: Curb your enthusiasm kid, this is serious stuff.
Here, roll this pair of dice, but don't look at the the result. OK, good.
Now without looking, tell me the probability that you rolled a seven.
If you're going to play craps this is important.
By the way, I can tell you that one of your dice is a four.
A: Hmm...
So I could have rolled 41 42 43 44 45 46 14 24 34 54 or 64,
all with equal likelihood, with 34 and 43 making seven.
That's a probability of 2/11.
P: You're on a roll kid, now let's do it again. Great.
Again without looking, what's the probability you rolled a seven?
By the way, I can tell you one of your dice is a one.
A: So I could have rolled 11 12 13 14 15 16 61 51 41 31 or 21,
with 16 and 61 making seven. Hmm... it's the same as before - 2/11.
P: And if I had told you one of your dice was a five?
A: Well ... I guess it really doesn't matter what number you tell me.
It will always come out the same. The probability will be 2/11.
P: So what can we deduce from that?
A: That the probability of two dice making seven is ... 2/11.
But wait... Hey, you're not really Professor Plato, are you?
P: No. I'm an insurance salesman.
So ... what exactly is the probability of making seven?
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