Question

A box contains 12 red and 8 blue balls. Two balls are drawn randomly from the box without replacement. The probability of drawing a pair of balls having the same color is ________

Hint:

To find the probability of drawing two balls of the same color, calculate the favorable outcomes for each color and divide by the total possible outcomes.

Answer 1

Step 1: Total number of balls.
The total number of balls in the box is: \[ 12 + 8 = 20 { balls}. \] The total number of ways to draw two balls from 20 is given by: \[ \binom{20}{2} = \frac{20 \times 19}{2} = 190. \] Step 2: Number of favorable outcomes for drawing two red balls.
The number of ways to choose 2 red balls from 12 is: \[ \binom{12}{2} = \frac{12 \times 11}{2} = 66. \] Step 3: Number of favorable outcomes for drawing two blue balls.
The number of ways to choose 2 blue balls from 8 is: \[ \binom{8}{2} = \frac{8 \times 7}{2} = 28. \] Step 4: Total number of favorable outcomes.
The total number of favorable outcomes is: \[ 66 + 28 = 94. \] Step 5: Calculating the probability.
Thus, the probability of drawing two balls of the same color is: \[ P({same color}) = \frac{94}{190} = 0.4947. \] So, the probability, rounded off to three decimal places, is: \[ \boxed{0.495}. \]