What is the probability? Is it independent?

AI Thread Summary
The discussion revolves around the concept of probability and whether certain events are independent. One participant suggests that the probability of an event is 0.5, indicating a belief in independence. Another participant challenges this by prompting a deeper analysis of possible outcomes involving boys and girls. The conversation emphasizes the need for clarity on what is meant by "independence" in this context. Overall, the thread highlights the complexities of probability and the importance of examining all possible scenarios.
Amlan mihir
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Homework Statement

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The Attempt at a Solution

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I think it is independent event so , the probability would be 0.5 . correct if me i am wrong please.
 

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Hello Amlan, :welcome:

Look at all the possibilities: two boys, one boy one girl, one girl one boy, two girls.
How many of those have one girl ?
How many of those have two girls ?
You refer to independency. What independency, precisely ?

Or am I playing advocate of the devil ? That's PF for you :smile:
 
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Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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