Question

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 or orange. p(purple or orange) = simplify your answer completely.

Explanation:

Step1: Calculate the total number of balls

The total number of balls is the sum of blue, purple, red, and orange balls.
$$19 + 28+21 + 29=(19 + 21)+(28 + 29)=40+57 = 97$$

Step2: Calculate the number of purple or orange balls

The number of purple balls is \(28\) and the number of orange balls is \(29\). So the number of purple or orange balls is \(28 + 29=57\)

Step3: Calculate the probability

The probability \(P(\text{purple or orange})\) is the number of purple or orange balls divided by the total number of balls.
$$P(\text{purple or orange})=\frac{57}{97}$$

Answer:

\(\frac{57}{97}\)