Question

do you know how?

1. a bag contains 40 marbles. eight are green,

and 2 are blue. you select one marble at
random. what is the probability of each event?
a. the marble is green or blue.
b. the marble is not green and not blue.

Explanation:

Step1: Calculate the number of favorable outcomes for part a

The number of green marbles is \(8\) and the number of blue marbles is \(2\). The number of favorable outcomes for the marble being green or blue is \(8 + 2=10\).

Step2: Use the probability formula \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\) for part a

The total number of marbles is \(n = 40\). So \(P(\text{green or blue})=\frac{10}{40}=\frac{1}{4}\)

Step3: Calculate the number of favorable outcomes for part b

The number of marbles that are not green and not blue is \(40-(8 + 2)=30\)

Step4: Use the probability formula \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\) for part b

So \(P(\text{not green and not blue})=\frac{30}{40}=\frac{3}{4}\)

Answer:

a. \(\frac{1}{4}\)
b. \(\frac{3}{4}\)