What is your intuition about this probability comparison?
9
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0.2
0.169

We have two different independent potential events A and B.

Somebody sais: "Probability of A is 0.02. Event B is ten times more likely than A."

What number comes to your mind as probability of B?

1) "Multiply the absolute value". 0.02*10=0.2

2) "Multiply the chances". There were 50 "tickets in a hat" and only one of them was suitable for event A, 49 invalid. (0.02=1/(49+1)). We multiply the suitable tickets and don't touch any other.

10/(49+10)=10/59=0.169

This question is just about how you interpret the phrase "more likely".

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Same question with higher probabilities. Curious if people's intuition is different with higher initial probabilities:

@Toby96 https://manifold.markets/Toby96/what-is-your-intuition-about-this-p-c937e06a9ba2

What is your intuition about this probability comparison?
This is essentially the same question as https://manifold.markets/KongoLandwalker/what-is-your-intuition-about-this-p but with higher initial probability (ie. closer to 1). We have two different independent potential events A and B. Somebody sais: "Probability of A is 0.5. Event B is two times more likely than A." What number comes to your mind as probability of B? 1) "Multiply the absolute value". 0.5*2=1 2) "Multiply the chances". There were 50 "tickets in a hat" and only 25 of them was suitable for event A, 25 invalid. (0.5=25/(25+25)). We multiply the suitable tickets and don't touch any other. 50/(50+25)=50/75=2/3 This question is just about how you interpret the phrase "more likely". [link preview]

@Toby96 i was planning to do the same.

The questioned appeared when i saw relations between 2 unknown probabilities. What if one of them appears to be 0.9 when the other was said to be thrice bigger? Either the equation falls apart or the ticket reasoning was used.

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