To find the probability that a randomly picked ball is purple from a bag containing several balls of different colors, we follow these steps:
1. Determine the total number of balls in the bag:
- There are 19 blue balls.
- There are 28 purple balls.
- There are 21 red balls.
- There are 29 orange balls.
To find the total number of balls, we simply add these numbers together:
[tex]\[
\text{Total number of balls} = 19 + 28 + 21 + 29
\][/tex]
Adding these numbers gives:
[tex]\[
19 + 28 + 21 + 29 = 97
\][/tex]
So, the total number of balls in the bag is 97.
2. Determine the number of favorable outcomes:
- The favorable outcome in this case is picking a purple ball. The number of purple balls is 28.
3. Calculate the probability:
- The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
The formula for probability is:
[tex]\[
P (\text{purple}) = \frac{\text{Number of purple balls}}{\text{Total number of balls}}
\][/tex]
Substituting in the values we found:
[tex]\[
P (\text{purple}) = \frac{28}{97}
\][/tex]
4. Determine the numerical value of the probability:
- Performing the division:
[tex]\[
\frac{28}{97} \approx 0.28865979381443296
\][/tex]
So, the probability [tex]\( P(\text{purple}) \)[/tex] that a randomly picked ball is purple is approximately:
[tex]\[
P (\text{purple}) \approx 0.2887
\][/tex]
