Question 1201361
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Suppose Dan wins 40% of all his chess games.
If Dan is to play 4 games, what is the probability Dan wins at least one game?
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<pre>
The event that Dan wins at least one game is the COMPLEMENT to the event that Dan 
loses all 4 games.


For this complementary event, the probability is  P = {{{(1-0.4)^4}}} = {{{0.6^4}}} = 0.1296.


Therefore, the answer to the problem's question is  

    1 - {{{(1-0.4)^4}}} = 1 - {{{0.6^4}}} = 1 - 0.1296 = 0.8704.
</pre>

Solved.