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Area model guide

Mark the same-colour rectangles:
Step 1 of 2
  • The bag holds 3 red marbles and 2 blue; two are drawn, without putting back.
  • The square’s area is 1.
  • The first draw cuts it into strips as wide as their probabilities: 35\displaystyle \frac{3}{5} red, 25\displaystyle \frac{2}{5} blue.
  • The second draw cuts each strip across, as high as its probabilities after the first.
  • The event: both marbles are the same colour. A tap marks a rectangle; Check says whether the marks are right.
  • A rectangle’s area is its width times its height: 35⋅24=620\displaystyle {\frac{3}{5}\cdot\frac{2}{4}}={\frac{6}{20}}.
  • That is the probability of its two outcomes – the same product as along the tree’s path.