Probobility of inheritance while sister is negative.

[ProbobilityNewbie]

A father has a crooked gene. Its 50% chance for child to inherit it (eighter he/she inherits it from father or he inherits it from mother who has a normal gene).
A child has a sister. Sister got the results back and she is negative on the bad gene - she doesent have it.

What does that mean for the child? Is the probobility the child has a crooked gene 25% or is it still 50%??

Also one more similar question of the same type of problem I think: if one plays a roulette (and lets omitt the green space), he has a 50% chance to land on red.
He plays 10 rounds and he landed on 10 straight black fields.
Is the probobility he will land on red with his 11th throw 99,95% (1 - (1/2 on the power of 11)) or is it still 50% because I have to look at it as the brand new throw?

 

[Dr.Peterson]

A father has a crooked gene. Its 50% chance for child to inherit it (either he/she inherits it from father or he inherits it from mother who has a normal gene).
A child has a sister. Sister got the results back and she is negative on the bad gene - she doesn't have it.

What does that mean for the child? Is the probability the child has a crooked gene 25% or is it still 50%??

The question is overlooking some important aspects of genetics; I'm going to guess that it isn't from a textbook, but you made it up without the required knowledge of the subject. If a textbook asked this question, I'd get rid of it.

If genes worked as you imply (everyone has just one gene for a given condition, which comes from either father or mother), then what the sister has would be irrelevant to what you get. See below.

But in reality (and even this is oversimplified) you have two copies of a given gene, one from the father and one from the mother; and their effects depend on whether it is dominant or recessive. In some such situations, the fact that the sister tests negative could tell you something about the nature of the father's genes that is not known just from his having the disease, so it could change your probabilities. I won't attempt to explain this fully; but here's an intro to some of the issues.

Also one more similar question of the same type of problem I think: if one plays a roulette (and let's omit the green space), he has a 50% chance to land on red.
He plays 10 rounds and he landed on 10 straight black fields.
Is the probability he will land on red with his 11th throw 99,95% (1 - (1/2 on the power of 11)) or is it still 50% because I have to look at it as the brand new throw?

Does the ball or the wheel have a memory? No. It's a new throw. To learn about this, look up "gambler's fallacy".

On the other hand (and somewhat related to my answer about how genetics really works), if you get red 10 times in a row, you might want to check for evidence of cheating.

 

[ProbobilityNewbie]

Thank you for your kind and informative answer.

Kind Regards