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/sci/ - Science & Math

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7554137 No.7554137 [Reply] [Original]

Question because I'm bad at probabilities:

Suppose I have two separate lights attached to buttons. If I press the left button, the left light turns red with a probability of 0.75 or it turns green with a probability of 0.25. On the other hand, if I press the right button, the right light turns red with a probability of 0.25 or it turns green with a probability of 0.75.

I get a box in the mail. It contains two more of these lights. Both are ensured to be identical, but I don't know if they're the red version or the green version. If I press both buttons to check the lights, how confident can I say I am that the lights I got are red or green?

My idea is to multiply the probabilities together. If I see red on the first light, that's 0.75. If I see red on the second light, that's 0.75*0.75. I don't think this is right though, because wouldn't that mean the probability decreases by multiplying them together?

>> No.7554143

How can you be confident about the color when it can be either of them?

>> No.7554153

>>7554137
The probability of two independent events occurring in series dies reduce the probability that's why p*p results in a lower probability

>> No.7554163

>>7554143
Sorry, I should rephrase. I meant my confidence that the light is either a red light or a green light, since one colour has a higher probability of showing compared to the other.

>> No.7554165

>>7554153
I could understand this if you were talking about something like a die, where each side has an equal probability of showing. But my question involves unequal probabilities. Would your idea still apply?

>> No.7554193

>>7554163
Assuming you can only use each light switch once (otherwhise you could switch the lights on and off 100 times and be certain about it).

I think it's best to approach each outcome differently. When you end up with 2 light bulbs being the same colour you are certain that one is their 'right' colour and the other one is the 'wrong'. But telling which light bulb is the right colour and which one is the wrong is only possible with a 0.5 probability.

When you have two different colors you can be sure that either:
-They're both their 'right' colour
-They're both their 'wrong' colour
(One being the right and one being the wrong is the situation with same colours).

The former has a probability of 0.75*0.75 of happening while the latter has a probability of 0.25*0.25 of happening. So I'd say being confident about their colour is only possible with a 0.75*0.75 probability.

>> No.7554228

>>7554193
I think I have to correct myself here.

In the second situation with two different colours you're sure that they're both wrong or both right, you can rule out the other situations with one being right and one being wrong.

The probability of them both being right is 0.75*0.75=0.56 while them both being wrong has a chance of 0.25*0.25=0.006. Now I think you have to correct for being able to rule out the 2 outcomes of one being wrong and one being right. The total chance of ending up with different colours is 0.56+0.006=0.566. But when you already know that you have two different colours either the situation with a probability of 0.56 or 0.006 happened. Therefore there is a 99% chance you're guessing the right outcome.