Percentage Probability

[Sacha Singh]

Hi All,

If I had a 70% chance of accomplishing that goal but I had 3 attempts to accomplish it, what is my overall chance of success? I'm thinking it goes up but not sure by what percentage. Pls help.

Sacha

 

[tkhunny]

"goes up" from what? Because of what?

Question is ambiguous. I'll answer two ways.


If you had a 70% chance of success, given three tries, then you had a 30% chance of failure, given 3 tries. Thus, your overall chance of failure gives: [math]\left[p(Failure\;on\;one\;try)\right]^{3} = 0.30\;\rightarrow\;p(Failure\;on\;one\;try) = 0.67\;thus,\;p(success\;on\;one\;try) = 1 - 0.67 = 0.33[/math]
That seems to be more in line with what you SAID, but it may not be what you MEANT.

If you MEANT, [math]p(success\;on\;one\;try) = 0.70,[/math] then [math]p(failure\;on\;one\;try) = 1 - 0.70 = 0.30[/math]. Thus, [math]p(failure\;given\;three\;tries) = 0.30^{3} = 0.027[/math] and we have [math]p(success\;given\;three\;tries) = 1 - 0.027 = 0.973[/math]
It's important to be clear.

 

[Dr.Peterson]

If I had a 70% chance of accomplishing that goal but I had 3 attempts to accomplish it, what is my overall chance of success? I'm thinking it goes up but not sure by what percentage. Pls help.

I'll try a second interpretation. Suppose you meant this:

If I have a 70% chance of accomplishing a goal on any one try, but I have 3 attempts to accomplish it, what is my overall chance of success?​

Then the probability of succeeding on any one of the three tries is 1 minus the probability of failing on all three.

The probability of failing on one try is [MATH]1 - 0.70 = 0.30[/MATH].

The probability of failing on all three is [MATH]0.30^3 = 0.027[/MATH].

So the probability of succeeding at least once is [MATH]1 - 0.027 = 0.973 = 97.3\%[/MATH]. Yes, that's a significant improvement.

You'll notice that this is just tkhunny's work turned inside out.

 

[Steven G]

Assuming that the 70% was for one try. Then of course the probability will increase if you get more chances.