Hello! I'd be happy to help you with this probability exercise.
a) To create the sample space, we need to list all possible outcomes. In this case, we have 10 balls numbered from 11 to 20, with some being red and others green. The sample space, denoted as S, would look like this:
S = {11R, 12R, 13R, 14R, 15R, 16R, 17R, 18R, 19R, 20R, 11V, 12V, 13V, 14V, 15V, 16V, 17V, 18V, 19V, 20V}
This includes all possible combinations of numbers (from 11 to 20) and colors (red and green).
b) The probability of getting a even number can be calculated by counting the favorable outcomes and dividing by the total number of outcomes. In this case, the even numbers between 11 and 20 are 12, 14, 16, 18, and 20. There are 5 even numbers out of 20 total outcomes. Therefore, the probability of getting an even number is 5/20 or 1/4.
c) If the probability of drawing a green ball is 3/5, it means that out of every 5 balls drawn, 3 will be green. This implies that there are 3 green balls for every 5 balls in the bag. Since there are a total of 10 balls in the bag, you can calculate the number of green and red balls based on this ratio. Let G be the number of green balls and R be the number of red balls. You have:
G/(G+R) = 3/5
G + R = 10
By solving these equations simultaneously, you can find the number of green and red balls in the bag.
I hope this helps you understand how to approach these probability problems! Let me know if you need further clarification.
