For the math you would do 2/3 mutipled by 1/2. You do 2/3 because the colors red and blue are also in bag 2. Which is why it's 2/3. As for the bag 2 the colors red and blue are the only ones inside therefore you only choose 1/2. The reason why you only choose 1 is because the question is asking for the theoretical probability of the same color from both bags. And for bag number 1 there's a total of 3 marbles and bag number 2 there's a total of 2 marbles.
Inside of the bag 1 there are 3 marbles colored green, red and blue and in bag number 2 there are 2 marbles colored red and blue.
The theoretical probability is 1/3
Question 2 explanation
The results that you get are always random you can't really choose the outcome unless you cheat.
Just because the 10/30 is the amount of wins that you should get dosent mean its exactly going to happen. In this case they got 9 out 30 wins, you can't control probability
Question 3 explanation
Like before there are 4 gold,4 red,1 blue and nine in total inside the spinner. So that means there's a greater probability. So its 4/9 for gold, 4/9 for red and 1/9 for blue. So because there's a greater probability it gives you a better chance of winning. You can also see the spinner, but inside a bag you cant
Inside the spinner there are 4 gold, 4 red and 1 blue sections
In the bags the theoretical proabbaility was only 1/3 compared to the probability of 4/9, all you do is compare the two and 4/9 is greater