A bag contains 10 red, 15 white, 25 green balls. What should be the minimum number of balls drawn without replacement so that you get 5 red, 3 white, 10 green balls.
In order to guarantee any reds at all, you need to draw 41, since the first 40 might be all green and white.
So, 45 draws will guarantee 5 reds.
To determine the minimum number of balls that need to be drawn without replacement to obtain a specific combination of balls, you can use the concept of combinations.
In this case, you want to get 5 red, 3 white, and 10 green balls from the bag that contains 10 red, 15 white, and 25 green balls.
To guarantee this specific combination, you need to consider the worst-case scenario. This means assuming that you draw the maximum number of balls of each color before obtaining the desired amounts.
So, first, let's calculate the maximum number of balls you can draw for each color individually:
- Maximum number of red balls: You need 5 red balls, so you will have to draw all 10 red balls from the bag.
- Maximum number of white balls: You need 3 white balls, so you will have to draw all 15 white balls from the bag.
- Maximum number of green balls: You need 10 green balls, so you will have to draw all 25 green balls from the bag.
Now, to determine the minimum number of balls that need to be drawn, you add up the maximum number of balls for each color:
10 red balls + 15 white balls + 25 green balls = 50 balls
Therefore, the minimum number of balls that need to be drawn without replacement is 50.
However, it's important to note that the actual number of balls you need to draw may be less than 50 in practice, depending on the specific arrangement of balls in the bag. The worst-case scenario assumes that you draw the maximum number of balls required for each color before reaching the desired amounts.