Question 43·Easy·Probability and Conditional Probability
A jar contains only red, white, and black beads. The jar has 18 red beads, 12 white beads, and 30 black beads.
If one bead is selected at random from the jar, which of the following represents the probability that the bead will be either red or white?
For probability questions on the SAT, quickly translate the situation into a fraction: numerator = number of favorable outcomes, denominator = total number of equally likely outcomes. Carefully read phrases like "either A or B" and add the counts for all listed favorable categories (since you are selecting only one item, these events are mutually exclusive). After forming the fraction, check whether it needs simplifying or whether the choices already use a common denominator so you can match it directly.
Hints
Write the probability as a fraction
Probability can be written as . Identify what counts as a favorable outcome and how many total beads there are.
Identify favorable outcomes
"Either red or white" means any bead that is red or any bead that is white. How many beads are there of those two colors combined?
Check the denominator
All the answer choices have denominator 60. Verify how many total beads are in the jar to see why 60 is the correct denominator.
Desmos Guide
Compute the probability fraction in Desmos
In Desmos, type (18+12)/(18+12+30) and press Enter. This expression represents the probability of selecting a red or white bead, as favorable outcomes over total outcomes.
Compare with the answer choices
In separate lines, type 12/60, 18/60, 30/60, and 48/60. Compare each of these values to the result of (18+12)/(18+12+30) and choose the option that has the same value.
Step-by-step Explanation
Find the total number of beads
The jar contains 18 red beads, 12 white beads, and 30 black beads.
Add them to find the total number of beads:
So there are 60 beads in the jar.
Count the beads that are red or white
We want the probability that a bead is either red or white.
That means we count all beads that are red or white (both colors are favorable outcomes):
So there are 30 favorable beads (red or white).
Form the probability and match it to an answer choice
Probability is
Here, that is
Among the answer choices, this corresponds to choice C) , which is the correct answer.