Probability of Drawing Red Balls

This question involves calculating the probability of a specific event happening, which is drawing a red ball from a bag containing balls of different colors. Probability helps us understand the likelihood of an event occurring.

Understanding the Ball Counts

First, let's identify the key information given in the problem:

• Number of red balls in the bag = 4
• Number of blue balls in the bag = 6

Calculating the Total Number of Balls

To find the probability, we need the total number of balls in the bag. This represents the total possible outcomes when drawing one ball.

Total number of balls = (Number of red balls) + (Number of blue balls)

Total number of balls = 4 + 6 = 10

Calculating the Probability of Drawing a Red Ball

The probability of an event is calculated using the formula:

$ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} $

In this case:

• The favorable outcome is drawing a red ball.
• Number of favorable outcomes (red balls) = 4
• Total number of possible outcomes (total balls) = 10

Now, we can plug these values into the formula:

$ P(\text{Red Ball}) = \frac{\text{Number of red balls}}{\text{Total number of balls}} $

$ P(\text{Red Ball}) = \frac{4}{10} $

Step-by-Step Solution

1. Identify favorable outcomes: The number of red balls is 4.
2. Identify total outcomes: The total number of balls is 10 (4 red + 6 blue).
3. Calculate probability: Divide the number of favorable outcomes by the total number of outcomes.
4. Calculation: $ \frac{4}{10} $
5. Simplify: $ \frac{4}{10} $ simplifies to 0.4.

Final Probability

Therefore, the probability of drawing a red ball from the bag is 0.4.