Let's break this down step by step.
The problem tells us two things:
1. There are twice as many red marbles as blue marbles.
2. There are twice as many blue marbles as green marbles.
The easiest approach is to pick a simple number for green marbles and build from there.Let's say there are
1 green marble.
Since there are twice as many blue as green:
Blue =
2 ×
1 =
2 marbles
Since there are twice as many red as blue:
Red =
2 ×
2 =
4 marbles
Now add them all up:
Total =
4 +
2 +
1 =
7 marbles
The
probability of picking a blue marble = Blue / Total =
2 /
7Answer: DA common mistake here is mixing up the ratios. For example, if you accidentally read it as "twice as many blue as red" (instead of twice as many red as blue), you'd get blue =
4, red =
2, green =
1, and the probability would be
4/7 — which isn't even an answer choice, so that would be a signal to re-read the problem.
Key Principle: When a problem gives you ratios between quantities, assign the smallest group a simple value (like 1) and build the other quantities from there. This makes the math clean and fast.