A bag contains 19 blue, 28 purple, 21 red, and 29 orange balls. You pick one ball at random.

Find the probability that it is purple.

[tex]\[ P(\text{purple}) = ? \][/tex]



Answer :

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]