What is the probability that they are of same color ? . Enter the answer correct to two decimal places.

To answer your question about the probability that two items are of the same color, I'll need a bit more context, such as the total number of items, the distribution of colors among them, or whether you're drawing with or without replacement. Without specific details, I can provide a general framework for solving this type of probability question.

Example Problem

Assuming there are two colors (let's say Red and Blue), and you have:

• 3 Red balls
• 2 Blue balls

Break Down the Problem

1. Count the total number of items.
2. Identify the favorable outcomes for selecting two items of the same color.

Relevant Concepts

• The total number of ways to select 2 items from the total is given by the combination formula:

$C(n, r) = \frac{n!}{r!(n-r)!}$

Where:

• $n$ = total number of items
• $r$ = number of items to choose

Analysis and Detail

1. Total Number of Items:

   • Total balls = 3 Red + 2 Blue = 5 balls.

2. Total Ways to Choose 2 Balls: $C(5, 2) = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10$

3. Favorable Outcomes (Choosing Same Color):

   • Choosing 2 Red Balls: $C(3, 2) = \frac{3!}{2!(3-2)!} = \frac{3 \times 2}{2 \times 1} = 3$

   • Choosing 2 Blue Balls: $C(2, 2) = \frac{2!}{2!(2-2)!} = \frac{2}{2 \times 1} = 1$

   • Total favorable outcomes = 3 (Red) + 1 (Blue) = 4.

Verify and Summarize

Probability of selecting two balls of the same color: $P(\text{same color}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{10} = 0.4$

Final Answer

The probability that they are of the same color is 0.40.