Statistics Question

[mathgalpsu]

I am briefly explaining geometric prob. to my class. We used two dice and
rolled until we got double 6's. The students understand that the
probability of getting it on the first roll is 1/36, the second is
(5/36)*(1/36), etc. I explained when we did the pdf that each time we are
multiplying by a number less than 1, so as n gets larger, the prob.
becomes less (we were looking at a histogram). They understood that until
we got to mean. When they found that the mean is 36, they got confused.
They are asking, "Shouldn't the probability at X=36 be higher than at
X=1?" (Which was a point I made during binomial prob.) I explained again
about multiplying by a number less than 1. They got the math, but it
isn't intuitive. The pdf indicates that there is a higher probability of
getting double 6's on the first roll than on the second, third,
thirty-sixth, etc. I don't really know what to say. Am I explaining it
(or understanding it) incorrectly? This is the first time I've taught
this class from this book.

 

[stapel]

It's not just "the chance of getting double sixes on the X-th roll"; you're computing "the chance of getting double sixes on the X-th roll given than you haven't gotten double sixes on any of the previous rolls".

In other words, instead of looking at the options for one roll (one in thirty-six), you're looking at the options for X rolls (one in, well, lots more). Because of that prior condition, the odds are much lower.

I think the odds would perhaps be more intuitive if you considered "the chance of getting double sixes at some point in X rolls".

Eliz.

 

[pka]

If we roll 72 times with no double sixes, the probability of rolling double sixes on the 73rd time is still 1/36.

Ask your students this:
“If we roll a pair of dice 72 times, how many double sixes should we expect”
Well the answer is 2. Why? (1/36)(72)=2
In 360 rolls expect 10. Right?

If we flip a coin 50 times we expect 25 heads? WHY?
Suppose that an event happens with probability p. If we do N independent trials we expect the event to happen p*N times