Question 37·Easy·Probability and Conditional Probability
A jar contains 12 red marbles and 8 blue marbles. If one marble is selected at random from the jar, what is the probability that the marble selected is blue?
For single-step probability questions, quickly count the total number of outcomes and the number of favorable outcomes, then write probability as favorable/total. Always simplify the fraction to lowest terms to match the choices and check that your answer is between 0 and 1, since any probability outside that range is automatically wrong.
Hints
Think about the total number of possible outcomes
First, figure out how many marbles are in the jar altogether. This will be the denominator of your probability fraction.
Identify the favorable outcomes
How many marbles in the jar are blue? That number will be the numerator of your probability fraction.
Form and simplify the probability
Write probability as (number of blue marbles) over (total number of marbles), then simplify the fraction if possible to match one of the answer choices.
Desmos Guide
Use Desmos to compute and simplify the fraction
In a new expression line, type 8/(12+8) and press Enter. Look at the simplified fraction that Desmos shows; that is the probability in simplest form.
Step-by-step Explanation
Find the total number of marbles
Add the red and blue marbles together:
So there are 20 marbles in total.
Write the probability as a fraction
Probability of an event = (number of favorable outcomes) (total number of outcomes).
Here, the favorable outcomes are the blue marbles, so there are 8 favorable outcomes.
Write the probability as a fraction:
Simplify the fraction and match to an answer choice
Simplify by dividing the numerator and denominator by their greatest common factor, 4:
So the probability that the marble selected is blue is , which corresponds to choice C.