A jar-draw question is a probability question: count the beads you want, then count every bead that could be drawn. Add the color counts to find the total, and use Desmos to check the arithmetic. The tempting mistake is to divide by another color’s count, even though the draw is from the whole jar.
Hints
- Hint 1
The sample space is every bead that could be selected. Because the draw is from the whole jar, add the counts for all three colors to find the denominator.
- Hint 2
The favorable outcomes are the beads whose color matches the question. Put the blue count over the total you found, not over a different color’s count.
Step-by-step
Count blue beads over all beads
Step 1Find how many beads could be selected
The sample space is every bead that could be picked, so add all three colors. Type in Desmos; it shows beads in the jar.
- Step 2
Put the blue count over the total
The blue beads are the wanted outcomes. A probability is the number of wanted outcomes divided by the number of possible outcomes. Type in Desmos; it shows , which equals . So the probability of selecting a blue bead is . Choice C.