Handling Data 7
3 marks · NormalA bag contains 3 green counters and 2 yellow counters. Two counters are taken from the bag one after the other, without replacement.
Draw a tree diagram to show all the possible outcomes. Use your diagram to calculate the probability that both counters are green.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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\frac{3}{10} (±0.01)
Must show: Correct branches with labels and probabilities: G, Y; 3/5, 2/5, 2/4, 3/4
Also accept: 0.3
Common mistakes: Using 'with replacement' probabilities
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Draw correct tree diagram, labelling all branches with appropriate probabilities.
M2 · 1 mark · Correctly find probability path for GG (green then green): 3/5 × 2/4.
A1 · 1 mark · Obtain final answer: 3/5 × 2/4 = 6/20 = 3/10 or 0.3.
Worked solution
Tree diagram:
P(both green) = 3/5 × 2/4 = 6/20 = 3/10 or 0.3.