To solve the problem of finding the probability that a randomly drawn ball from a bag is either red or yellow, we need to follow these steps:
### Step 1: Determine the Total Number of Balls
First, let's find out the total number of balls in the bag. The bag contains:
- 4 red balls
- 3 blue balls
- 2 yellow balls
Adding these together gives us the total number of balls:
[tex]\[ 4 \, (\text{red}) + 3 \, (\text{blue}) + 2 \, (\text{yellow}) = 9 \][/tex]
So, there are 9 balls in total.
### Step 2: Determine the Number of Red Balls
Next, we look at the number of red balls, which is given as:
[tex]\[ 4 \][/tex]
### Step 3: Determine the Number of Yellow Balls
Similarly, we check the number of yellow balls, which is given as:
[tex]\[ 2 \][/tex]
### Step 4: Calculate the Probability of Drawing a Red Ball
The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability of drawing a red ball (P(Red)) is:
[tex]\[ P(\text{Red}) = \frac{\text{Number of Red Balls}}{\text{Total Number of Balls}} = \frac{4}{9} \][/tex]
### Step 5: Calculate the Probability of Drawing a Yellow Ball
Similarly, for the yellow balls, the probability of drawing a yellow ball (P(Yellow)) is:
[tex]\[ P(\text{Yellow}) = \frac{\text{Number of Yellow Balls}}{\text{Total Number of Balls}} = \frac{2}{9} \][/tex]
### Conclusion
So, summarizing our results:
1. The probability of drawing a red ball is:
[tex]\[ P(\text{Red}) = \frac{4}{9} \approx 0.4444 \text{ (or 44.44%)} \][/tex]
2. The probability of drawing a yellow ball is:
[tex]\[ P(\text{Yellow}) = \frac{2}{9} \approx 0.2222 \text{ (or 22.22%)} \][/tex]
