Quote:
Originally Posted by weehong
I captured the above idea, however I am confused why the following approach gives wrong answer:
Probability of all heads in 10 flips by one coin: p = 0.5^10
Probability of all heads in 10 flips by any of 1000 coin: 1000*p = 97.7%
In above I assumed there were 1000 10flips.

In order to multiply the probabilities in the "all" case, you need the events to be independent, and we have that for the coin flips. In order to add the probabilities in the "any of" case, you need the events to be
disjoint, i.e., they cannot simultaneously occur. The first coin giving 10 heads is not disjoint from the second coin giving 10 heads, so when you add their probabilities you are double counting the overlap which is "both coins giving 10 heads each."