Hello, I need help with this problem related to Bayes theorem.

Yesterday at the bar you met a man who said he worked in one casino of the city. According to the man, the casino has 2 types of slot machines and they are differentiated by the colour. Besides, he mentioned that one type of machines gives prizes in 10% of the games and the other type only gives prizes in 2%. However, the man didnt remember the colours of the machines. Next day you were to try your luck and you noticed that as the man said all the machines were painted red and blue. You took a coin from your pocket and played in the blue machine but you did not receive any prize. Again, you took a coin and decided to play one more time. Determine which is the best strategy: playing again in the blue machine o playinh in the red one.

And this one (but this is not bayes theorem).

The jurors for elections are randomly selected from a list of voters (n). In elections 25 people were selected, of which 15 were men and 10 women. Determine the probability of this event en each one of the following circumstance:

a) The list of the voters consists of the same part of men and women.

b) The list of voters consists of twice as many men as women.

c) The list of voters consists of twice as many women as men.

d) The proportion men-women is from 3 to 2. –> the professor said it was 3/5 of “n” men and 2/5 of “n” women.