A bag contains 33 balls: 10 blue 11 red and 12 green
If a person will select balls at random from the bag without replacement, what is the minimum number of balls needed to be selected in order to be sure that the balls selected include 3 balls of the same color
There are only 3 colors. So, after 6 draws, it is possible to have two of each color.
The 7th ball must be the one which matches two of the others.
To determine the minimum number of balls needed to be selected in order to be sure that the balls selected include 3 balls of the same color, we need to consider the worst-case scenario.
Let's assume that the first two balls selected are different colors. In this case, we would need to select at least one more ball of each color before we are certain to have selected 3 balls of the same color.
The worst-case scenario would be if the first two balls selected are blue and red. In this case, we would need to select at least 1 more blue ball and 1 more red ball before we are certain to have selected 3 balls of the same color.
So far, we would have selected 2 blue balls, 2 red balls, and 0 green balls.
Now, to ensure that we have selected 3 balls of the same color, we would need to select at least 1 more ball. Since the maximum number of any color is 12, we would be guaranteed to have at least 3 balls of the same color after selecting a maximum of 3 balls.
Therefore, the minimum number of balls needed to be selected to be sure that the balls selected include 3 balls of the same color is 3.