Question

colors of marbles in a bag
color | number
red | 8
blue | 10
green | 22
total | 40
the table shows the number of different colors of marbles in a bag. if a marble is chosen at random from the bag, what is the probability that the marble will be blue?
a. \\(\frac{30}{40}\\)
b. \\(\frac{22}{40}\\)
c. \\(\frac{18}{40}\\)
d. \\(\frac{10}{40}\\)

Explanation:

Step1: Recall Probability Formula

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. For choosing a blue marble, the number of favorable outcomes (blue marbles) is the number of blue marbles, and the total number of possible outcomes is the total number of marbles.

Step2: Identify Values

From the table, the number of blue marbles is \( 10 \), and the total number of marbles is \( 40 \).

Step3: Calculate Probability

Using the probability formula \( P(\text{blue})=\frac{\text{Number of blue marbles}}{\text{Total number of marbles}} \), we substitute the values: \( P(\text{blue}) = \frac{10}{40} \).

Answer:

D. \(\frac{10}{40}\)