The complement helps when a question gives probabilities for some categories but asks for the missing one. If those categories are the only possible outcomes, their probabilities add to . Subtract the known shares, then multiply the remaining share by the total count. Multiplying a given color’s probability by the total finds that color, not the missing one.
Hints
- Hint 1
The complement of choosing blue or red is choosing green because there are no other colors. All possible outcomes together have probability . What share remains after the two given probabilities?
- Hint 2
A probability is a part of the whole, not a marble count. Once you know the green share, multiply it by all marbles to find the number of green marbles.
Step-by-step
Find the missing probability, then the count
Step 1Write the green probability
The jar contains only blue, red, and green marbles. Green is the complement of blue or red: it covers everything those two colors don’t. The probabilities of all possible colors add to , so .
- Step 2
Calculate the green share
Type in Desmos. It shows , so one-quarter of the marbles are green. Don’t subtract those probabilities from : probabilities are shares, not counts.
- Step 3
Find the number of green marbles
A probability is the color’s count divided by the total, so multiply the green share by all marbles: . Type in Desmos. It shows , so there are 45 green marbles. Choice B.