Question 207618
A deck of 40 cards contains 10 green cards, 29 blue cards, and 1 red card. 
The first card you draw is the red card.
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So what you have now is a deck of 39 cards containing 10 
green cards and 29 blue cards.
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You draw 6 other cards without replacement.
What is the probability that at least one of those 6 cards is green?
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We use the complement event, and then subtract its probability from 1.

The complement event is to draw 6 non-green cards in a row.

There are 29 non-green cards, so the probability of drawing
a non-green card the first time is {{{29/39}}}.

Now there are 28 non-green cards, so the probability of drawing
a non-green card the second time is {{{29/38}}}.

Now there are 27 non-green cards, so the probability of drawing
a non-green card the third time is {{{29/37}}}.

Now there are 26 non-green cards, so the probability of drawing
a non-green card the fourth time is {{{29/37}}}.

Now there are 25 non-green cards, so the probability of drawing
a non-green card the fifth time is {{{29/36}}}.

Now there are 24 non-green cards, so the probability of drawing
a non-green card the sixth time is {{{28/35}}}.

So the probability of drawing a non-green card each of those
six times is the product of those probabilities

{{{(29/39)(29/38)(29/37)(29/36)(29/35)(29/34)=.2532145153}}}

Then {{{1-.2532145153=0.7467854847}}}

Edwin</pre>