Question

A bag contains 5 purple, 24 green, 12 yellow, and 18 gray marbles. A marble is drawn at random. What is the theoretical probability, as a decimal, of drawing a green marble? Round the decimal to the nearest hundredth.

Answer 1

`|\Omega|=59\\|A|=24\\\\P(A)=(24)/(59)\approx0.41`

Answer 2

p(event) = (number of ways desired outcome can happen)/(total number of outcomes)

The total number of outcomes is based on drawing any marble of any color. It is the the total number of marbles which is 5 + 24 + 12 + 18 = 59.

The desired outcome is to draw a green marble. Since there are 24 green marbles, the number of desired outcomes is 24.

p(green) = 24/59

p(green) = 0.406779...

Answer: 0.41