Question about "Poker Odds and Outs" chart

[SnowFog]

My first FTR question.

The chart gives the percentages of hitting on the turn or river based on the number of outs you have. The numbers for hitting on the river check out but I'm getting different results when I calculate the odds for hitting on the turn or river.

For example:
With 8 outs, it gives 17.4% as the chance of hitting on the river. Same as what I got. But it gives the chances of hitting on either the turn or the river as 31.5%.

This part I don't understand. Here is how I calculated.

Hitting on the turn: 8/47 = 17%
Hitting on the river: 8/46 = 17.4%

So I figured the chance of hitting on either is the sum of the 2, or 34.4%, not 31.5%.

I know it is a minor issue but I want to understand the calculations before I just memorize them. Does anyone know where I'm going wrong here. I figure it must be something I'm doing and not the charts or it would have been picked up on by know.

Rgds

[JL]

1 - [(47-outs/47) x (46 - outs/46)]
1 - (39/47) x (38/46)
....
you can do the rest

[givememyleg]

Here is the chart you are referring to - Pot Odds Chart - Texas Holdem Outs and Pot Odds Chart

You can't just add the percentages together, probability doesn't work that way - Probability - Wikipedia, the free encyclopedia

JL nailed it, just take

1 - (39/47) * (38/46) = 0.3145235892691950 or 31.5%.

Welcome to FTR!