bowl contain 3 white, 2 red and 4 blue balls? Two balls are selected at random. What are the chances that they can be: Are the two of the same color?
To find the chances of selecting two balls of the same color from a bowl containing 3 white, 2 red, and 4 blue balls, you need to calculate the probability of selecting two balls of the same color out of all possible combinations.
First, let's determine the total number of balls in the bowl:
Total number of balls = 3 white + 2 red + 4 blue = 9 balls.
Next, let's calculate the probability of selecting two balls of the same color:
1. Probability of selecting two white balls:
The number of ways to choose 2 white balls from 3 is given by the combination formula: C(3, 2) = 3.
The total number of ways to choose 2 balls from 9 is given by the combination formula: C(9, 2) = 36.
So, the probability of selecting two white balls is 3/36.
2. Probability of selecting two red balls:
The number of ways to choose 2 red balls from 2 is given by the combination formula: C(2, 2) = 1.
The total number of ways to choose 2 balls from 9 is 36.
So, the probability of selecting two red balls is 1/36.
3. Probability of selecting two blue balls:
The number of ways to choose 2 blue balls from 4 is given by the combination formula: C(4, 2) = 6.
The total number of ways to choose 2 balls from 9 is 36.
So, the probability of selecting two blue balls is 6/36.
Now, let's sum up all the probabilities of selecting two balls of the same color:
Probability of selecting two balls of the same color = Probability of selecting two white balls + Probability of selecting two red balls + Probability of selecting two blue balls
= 3/36 + 1/36 + 6/36
= 10/36
= 5/18.
Therefore, the chances of selecting two balls of the same color are 5/18, or approximately 0.2778 (rounded to four decimal places).