Percentages Question

[Blarg1480]

Hello Everyone,

I hope this is the correct place, i have a question thats bugging me. Out of school over 15 years, just something that popped up today.

I was working on a project where a system has a 35% accuracy, but would make 4 attempts at once. What would be the overall accuracy?

I believe i understand how to determine this via calculator (approx 86%), but for the life of me i couldn't remember how this calculation was done by hand. So i did some backwards math and got this but it feels overcomplicated. Can anyone tell me the proper formula and what its called?

.35×.35+.35 = 0.4725
.4725×.35+.35 = 0.637875
.637875×.35+.35 = = 0.8611

May be silly as its just something thats playing on my mind, but thanks for any help!

 

[Deleted member 4993]

Hello Everyone,

I hope this is the correct place, i have a question thats bugging me. Out of school over 15 years, just something that popped up today.

I was working on a project where a system has a 35% accuracy, but would make 4 attempts at once. What would be the overall accuracy?

I believe i understand how to determine this via calculator (approx 86%), but for the life of me i couldn't remember how this calculation was done by hand. So i did some backwards math and got this but it feels overcomplicated. Can anyone tell me the proper formula and what its called?

Some corrections to your calculation:

.35×.35+.35 = 0.4725
.4725×.35+.35 = 0.637875 ..........................incorrect. That should be 0.515375
0.515375×.35+.35 = = 0.53038125

.637875×.35+.35 = = 0.8611 ..........................incorrect.


What does 35% accuracy mean?

Does it mean that the system will be correct 35% time and will be wrong 65% time?​

What does overall accuracy in 4 tries mean?

Does it mean "% of time" that the system will be correct at least in one of those tries?​

 

[joshuaa]

you can use this formula

[MATH]A(1 + A)^{n - 1}[/MATH]
where [MATH]A[/MATH] is the accuracy of the system and [MATH]n[/MATH] is the number of attempts

 

[Blarg1480]

Some corrections to your calculation:

.35×.35+.35 = 0.4725
.4725×.35+.35 = 0.637875 ..........................incorrect. That should be 0.515375
0.515375×.35+.35 = = 0.53038125

.637875×.35+.35 = = 0.8611 ..........................incorrect.


What does 35% accuracy mean?

Does it mean that the system will be correct 35% time and will be wrong 65% time?

What does overall accuracy in 4 tries mean?

Does it mean "% of time" that the system will be correct at least in one of those tries?

Not sure how i messed that math up, ill just go with i was overtired at 4:00 am when i posted the message

In response to your question the system has a 35% chance of success for each attempt, but makes four separate attempts at a time. I was trying to determine of that sequence of 4 attempts, what would be the percentage of success after the sequence is complete.

Following my original long method with the corrected math it would be
0.35×0.35+0.35 = 0.4725
0.4725×0.35+0.35 = 0.515375
0.515375×0.35+0.35 = = 0.53038125

Meaning the sequence would have an overall 53% chance of success?

you can use this formula

[MATH]A(1 + A)^{n - 1}[/MATH]
where [MATH]A[/MATH] is the accuracy of the system and [MATH]n[/MATH] is the number of attempts

If i follow this formula:

[MATH]0.35(1 + 0.35)^{4 - 1}[/MATH][MATH]0.35(1.35)^3[/MATH][MATH]0.35(2.460375)[/MATH]
= 86%

Which is what i originally expected (when completed by calculator) but not what I'm seeing above, so little confused now.

Sorry, and thanks for the help!

 

[HallsofIvy]

Assuming that "35% accuracy" means it gets the correct answer 35% of the time then it does NOT get the correct answer 100- 35= 65% of time. Doing the calculation 4 times, you get the correct answer 35% of the time and an incorrect answer 65% of the time. The problem is distinguishing a correct answer from an incorrect answer!

There is only one correct answer while there are many incorrect answers. One method is to declare that if two or more of the answers are the same, then that is the correct answer. The probability of all four answers being incorrect (and presumably all different) is (0.65)^4= 0.17850625. The probability of 3 incorrect answers and one correct answer (so you cannot tell which is the correct answer) is 4(0.65)^3(0.35)= 0.384475. So the probability of either no correct answer or one correct answer (so no duplicates and you cannot tell which, if any, answer is correct) is 0.17850625+0.384475= 0.56298125 and the probability of two or more correct answers (which will be the same so you can tell they are correct) is 1- 0.56298125= 0.43701875, small but better than 35%.