A box containing 20 yellow balls, 9 red balls and 6 blue balls. If the balls are selected at random, what is the smallest number of balls that need to be selected so you will select at least two balls of each colour
probability - wise, the easiest pair to pick would be the yellow pair.
best case scenario:
you have picked 1 yellow, 9 reds and 6 blue.
So you definitely have a pair of blues , a pair of reds but no pair of yellows.
you have picked 16 balls.
So the 17st pick would have to be a yellow.
So minimum is 17
To determine the smallest number of balls that need to be selected in order to get at least two balls of each color, we can follow these steps:
1. Find the worst-case scenario to get the minimum number of balls.
2. Identify the first two colors that need to have at least two balls selected.
3. Determine the total number of balls needed to achieve this.
Let's go through these steps in detail:
Step 1: Find the worst-case scenario
In order to minimize the number of balls selected, we need to consider the worst-case scenario. This occurs when we select balls of the same color until we have two of each color.
Step 2: Identify the first two colors
Based on the given information, there are three colors: yellow, red, and blue. We need to identify the first two colors that need at least two balls selected.
The worst-case scenario would be if we select balls of the same color until we have at least two balls of that color. In this case, we need to ensure we have at least two yellow balls.
Step 3: Determine the total number of balls needed
To get at least two yellow balls, we need to select two yellow balls. After that, we will have two yellow balls. Since we also need at least two red balls and two blue balls, we need to select these as well.
So, the total number of balls needed to select at least two balls of each color would be:
2 (yellow) + 2 (red) + 2 (blue) = 6
Therefore, the smallest number of balls that need to be selected is 6.