Quote:
Originally Posted by paul99
Hi,
In reviewing some of the lectures, I have a question about Lecture 2 (slide 14; ~ 47 minute mark), "Coin analogy", how was 63% arrived at as the answer to the second question:
If you toss 1000 fair coins 10 times each, what is the probability that some coin will get 10 heads?
Thanks,
Paul

For each coin, probability of getting 10 heads is
which is approximately 0.001
Therefore, for each coin, the probability of not getting 10 heads is 1 minus that, approximately 0.999
The probability that none of the 1000 coins gets 10 heads is that to the power 1000, and we approximate
by
since the limit of
is
.
Finally, the probability that at least one coin will get 10 heads is one minus that, which is
and this is approximately 0.63.
PS: You can quote any part of the video lecture by using the lecture tags, in this case [lecture2] tag, as explained in the sticky thread about including a video segment.