Counts by color and one random pick signal a probability question: put the count you want over the count of everything that could be picked. Add the categories to find the whole group, then use Desmos to check the fraction. Counting the wrong color on top gives the probability of a different outcome.
Hints
- Hint 1
The sample space is every marble that could be picked. Since the pick comes from the whole jar, both red and blue marbles belong in the total. What do their counts add to?
- Hint 2
A favorable outcome is a pick that matches the question. Use the blue marble count on top of your fraction and the full-jar total on the bottom.
Step-by-step
Count blue marbles over all marbles
Step 1Count all possible picks
The sample space includes both colors because any marble in the jar could be picked. Type in Desmos; it shows marbles in all.
- Step 2
Put the wanted count over the total
A favorable outcome matches blue, so of the marbles count. Write the probability as . Putting on top would count red marbles instead.
- Step 3
Reduce the probability
Type on the next Desmos line. It shows ; tap the fraction button to see . Probability is the wanted count over the full count. So the probability of selecting a blue marble is . Choice C.