Fundamental odds/math calcuation question I don't get

[KHALI]

Say the situation is you flop nut str8 and opponent can only win by drawing to a flush. All betting is done and cards are all exposed. He has 9 outs to hit. Which means he has 9/45+9/44 which gives him about a 40.45% chance of hitting(correct?) .
My question is fundamentally why don't we think about the other guy as drawing to all the non-flush cards to figure out his odds. He has 36/45 cards that help him (80%) + 35/44 cards to help him(79%) . How can a player who is almost an 80% chance of hitting a helping card on either street only a 60% to win. Is it correct mathematics to combine the drawing odds. In theory the player with the straight is drawing to all the other cards so why don't we calculate it the same way?
Obviously I am not a math guy but I am curious as to why this works and is so readily accepted by most without question? Set me straight please.
Thanks

[BruceZ]

[ QUOTE ]
Say the situation is you flop nut str8 and opponent can only win by drawing to a flush. All betting is done and cards are all exposed. He has 9 outs to hit. Which means he has 9/45+9/44 which gives him about a 40.45% chance of hitting(correct?) .

[/ QUOTE ]

9/45 + (1 - 9/45)*9/44 = 36.36%


[ QUOTE ]
My question is fundamentally why don't we think about the other guy as drawing to all the non-flush cards to figure out his odds. He has 36/45 cards that help him (80%) + 35/44 cards to help him(79%) . How can a player who is almost an 80% chance of hitting a helping card on either street only a 60% to win.

[/ QUOTE ]

He must hit a helping card on both streets, and since it's 80% on each street, hitting on both is 80% * 80% = 64%.

[closer2313]

Those events are not mutually exclusive, so you just dont add the probability of hitting on the turn to the probability of hitting on the river. They both dont need to happen.

What you do is what Bruce said.

Probability of making it on the turn + (probability of missing on the turn * probability of making it on the river)

9/45 + (36/45)* 9/44 = 36.4%